(updated 10/1/2011)
This is a quick reference to common mathematical functions for the Hewlett Packard RPL calculators. In general, HP RPL calculators are classified into three families:
This table will focus on the HP 48S, 48G, and 50g - three of four models I actually own (I have a 49g+ which should be the same key mapping as the 50g. The 49G has a different mapping - and I do not own a 49G.)
Note: [LS] = left shift key (3rd key up from the ON button on the left side)
[RS] = right shift key (2nd key up from the ON button on the right side)
About Soft Keys
On the top row, there are six soft keys. The functions of these six keys change depending on what menu is currently active. The top row of the HP 49G, 49g+, and 50g are labeled as:
[F1] [F2] [F3] [F4] [F5] [F6]
On the HP 48S and 48G, these keys are not labeled - but I will still use the F# convention. So [F1] means first soft key from the left, [F2] means second soft key from the left, and so on.
Note: For the 50g, it is assumed that Soft Menus are turned on. (Flag -117 is set)
List of Functions
x^2
HP 48S/48G: [LS] [ √x ]
HP 50g: [LS] [ √X ]
x√y
HP 48S/48G: [RS] [√x]
HP 50g [RS] [√X]
10^x
HP 48S/48G: [LS] [y^x]
HP 50g: [LS] [EEX]
LOG
HP 48S/48G: [RS] [y^x]
HP 50g: [RS] [EEX]
e^x
HP 48S/48G: [LS] [1/x]
HP 50g: [LS] [Y^X]
LN
HP 48S/48G: [RS] [1/x]
HP 50g: [RS] [Y^X]
ABS
HP 48S: [MTH] [ F1 ] (PARTS) [ F1 ] (ABS)
HP 48G: [MTH] [F5] (REAL) [NXT] [F1] (ABS)
HP 50g: [LS] [ ÷ ]
ARG
HP 48S: [MTH] [ F1 ] (PARTS) [ F4 ] (ARG)
HP 48G: [MTH] [NXT] [F3] (CMPL) [F6] (ARG)
HP 50g: [RS] [ ÷ ]
ASIN
HP 48S/48G: [LS] [SIN]
HP 50g: [LS] [SIN]
ACOS
HP 48S/48G: [LS] [COS]
HP 50g: [LS] [COS]
ATAN
HP 48S/48G: [LS] [TAN]
HP 50g: [LS] [TAN]
->NUM
HP 48S: [RS] [EVAL]
HP 48G: [LS] [EVAL]
HP 50g: [RS] [ENTER]
->Q (Exact Answer)
HP 48S: [LS] [EVAL]
HP 48G: [LS] [ 9 ] (SYMBOLIC) [NXT] [F3]
HP 50g: [LS] [ 6 ] (CONVERT) [F4] (REWRI) [NXT] [F5] (->Q)
x!
HP 48S: [MTH] [F2] (PROB) [F3] (!)
HP 48G: [MTH] [NXT] [F1] (PROB) [F3] (!)
HP 50g: [LS] [SYMB] (MTH) [NXT] [F1] (PROB) [F3] (!)
COMB (Combination)
HP 48S: [MTH] [F2] (PROB) [F1] (COMB)
HP 48G: [MTH] [NXT] [F1] (PROB) [F1] (COMB)
HP 50g: [LS] [SYMB] (MTH) [NXT] [F1] (PROB) [F1] (COMB)
PERM (Permutation)
HP 48S: [MTH] [F2] (PROB) [F2] (PERM)
HP 48G: [MTH] [NXT] [F1] (PROB) [F2] (PERM)
HP 50g: [LS] [SYMB] (MTH) [NXT] [F1] (PROB) [F2] (PERM)
RAND (Random #)
HP 48S: [MTH] [F2] (PROB) [F4] (RAND)
HP 48G: [MTH] [NXT] [F1] (PROB) [F4] (RAND)
HP 50g: [LS] [SYMB] (MTH) [NXT] [F1] (PROB) [F4] (RAND)
% (Returns level 2 * level 1% on level 1)
HP 48S: [MTH] [F1] (PARTS) [NXT] [F4] (%)
HP 48G: [MTH] [F5] (REAL) [F1] (%)
HP 50g: [LS] [SYMB] (MTH) [F5] (REAL) [F1] (%)
%CHG (Percent Change from level 2 to level 1)
HP 48S: [MTH] [F1] (PARTS) [NXT] [F5] (%CH)
HP 48G: [MTH] [F5] (REAL) [F2] (%CH)
HP 50g: [LS] [SYMB] (MTH) [F5] (REAL) [F2] (%CH)
IP (Integer Part)
HP 48S: [MTH] [F1] (PARTS) [NXT] [NXT] [F3] (IP)
HP 48G: [MTH] [F5] (REAL) [NXT] [F5] (IP)
HP 50g: [LS] [SYMB] (MTH) [F5] (REAL) [NXT] [F5] (IP)
FP (Fraction Part)
HP 48S: [MTH] [F1] (PARTS) [NXT] [NXT] [F4] (FP)
HP 48G: [MTH] [F5] (REAL) [NXT] [F6] (FP)
HP 50g: [LS] [SYMB] (MTH) [F5] (REAL) [NXT] [F6] (FP)
To access the hyperbolic functions (SINH, COSH, etc..)
HP 48S: [MTH] [F3] (HYP)
HP 48G: [MTH] [F4] (HYP)
HP 50g: [LS] [SYMB] (MTH) [F4] (HYP)
Matrix Functions:
INV (Inverse)
HP 48S/48G: [1/x]
HP 50g: [1/X]
DET (Determinant)
HP 48S: [MTH] [F4] (MATR) [F5] (DET)
HP 48G: [MTH] [F2] (MATR) [F2] (NORM) [NXT] [F2] (DET)
HP 50g: [LS] [ 5 ] (MATRICES) [F2] (OPER) [F6] (DET)
M^T (Transpose)
HP 48S: [MTH] [F4] (MATR) [F3] (TRN)
HP 48G: [MTH] [F2] (MATR) [F1] (MAKE) [F3] (TRN)
HP 50g: [LS] [ 5 ] (MATRICES) [F2] (OPER) [NXT] [NXT] [F5] (TRN)
EGVL (Eigenvalues)
(not on the HP 48S)
HP 48G: [MTH] [F2] (MATR) [NXT] [F3] (EGVL)
HP 50g: [LS] [ 5 ] (MATRICES) [NXT] [F1] (EIGEN) [F3] (EGVL)
RREF
(not on the HP 48S)
HP 48G: [MTH] [F2] (MATR) [F3] (FACTR) [F1] (RREF)
HP 50g: [LS] [ 5 ] (MATRICES) [F5] (LIN S) [F4] (RREF)
Stack Functions:
Clear the Entire Stack
HP 48S: [RS] [backspace]
HP 48G: [LS] [DEL]
HP 50g: [RS] [Backspace]
Swap contents of levels 1 and 2
HP 48S: [LS] [right arrow] (SWAP)
HP 48G: [LS] [right arrow] (SWAP)
HP 50g: [LS] [right arrow] (unmarked)
Roll the entire stack down 1 level
(Move everything down one level and level 1 goes to stack n)
HP 48S: [PRG] [F1] (STK) [F6] (DEPTH) [F4] (ROLLD)
HP 48G: [LS] [up arrow] (STACK) [F6] (DEPTH) [F4] (ROLLD)
HP 50g: [LS] [EVAL] (PRG) [F1] [NXT] [F6] (DEPTH) [F2] (ROLLD)
Angle Conversions:
Degrees to Radians
HP 48S: [LS] [SPC] (π) [ x ] 180 [ ÷ ]
HP 48G: [MTH] [F5] (REAL) [NXT] [NXT] [F5] (D->R)
HP 50g: [LS] [SYMB] (MTH) [F5] (REAL] [NXT] [NXT] [F5] (D->R)
Radians to Degrees
HP 48S: 180 [ x ] [LS] [SPC] (π) [ ÷ ]
HP 48G: [MTH] [F5] (REAL) [NXT] [NXT] [F6] (R->D)
HP 50g: [LS] [SYMB] (MTH) [F5] (REAL] [NXT] [NXT] [F5] (R->D)
Friday, September 30, 2011
Common Keyboard Commands for Hewlett Packard RPL Calculators (HP 48S/48G/50g)
RPL Basics
RPL Basics
(updated 10/1/2011)
I dedicate this blog to Peter Murphy - thank you for the request!
This is a basic tutorial of reverse polish lisp (RPL). It is a combination of RPN (reverse polish notation), Lips, and Forth languages.
RPL removes the need to enter parenthesis during long calculations and allows for immediate feedback during calculations; you will not need to enter a long operation before getting feedback - thus eliminating errors. A lot of times, the number of keystrokes required to make a calculation is reduced using RPL compared to algebraic systems. RPL works like RPN, but there several differences.
All of the following calculators, manufactured by Hewlett Packard, operate on RPL: HP-28C, HP-48S, HP-48SX, HP-48G, HP-48G+, HP-48GX, HP-49G, HP 49g, HP 50g. Currently, only HP 50g is sold new. The rest can be found used (sometimes new) on other online vendors. There are also several emulators of RPL calculators (HP48+ for example) that can be used for the iPhone/iPod Touch/iPad and devices operating on Android.
There are two types of RPL: User and System. User RPL is for basic, everyday use. You can create programs with User RPL right on the calculator's keyboard. System RPL allows users to create faster and more efficient programs. However, System RPL programming is more difficult than User RPL - most of the time programs have to complied and then downloaded to the calculator. For our purposes of the tutorial, we will use User RPL ("Just use the keyboard"). You can find additional information on RPL on the HP Museum of Calculators' RPL Page.
The Stack
Typically, an RPL calculator uses a stack with an infinite amount of "levels" (or registers). Each level is stacked on top of another. The size of the stack is dynamic depending on the contents each level has. In my experience, I end up using 1 to 3 levels, but I can use as many levels as I want so long as I have memory. For example a four-level stack diagram looks like this:
4:
-------------------------------
3:
-------------------------------
2:
-------------------------------
1:
-------------------------------
The 28C displays 3 levels, the HP 48S and 48G series display 4 levels, and the HP 49G series, including the 49g+ and 50g can display any number depending on the screen's font setting. Typically, FONT 8 shows 7 levels.
What is required of the user to execute a desired operation depends on the number of arguments (for our purpose, numbers) the function requires. Most calculator functions require one or two arguments.
One-argument functions operate on whatever is in level 1, sometimes referred to as X register. For one-argument functions, simply execute the desired operation. One-argument functions include all the trigonometric functions (sine, cosine, tangent), logarithms, exponential (e^), reciprocal, square root, and factorial (x!). The change sign operation fits under the category of one-number operations because it simply multiplies the number by -1. The change sign operation is labeled [ +/- ].
Two-argument functions operate on the contents of levels 2 and 1. Level 2 is like the Y register and level 1 the X register. Common two-argument functions include the arithmetic operators (+, -, x, ÷), powers (y^x), combination and permutations, percent and percent change (Δ%). To use a two-argument function, enter the first number (y), then press ENTER. ENTER terminates the entry and gets the calculator ready to receive another number. Next, enter the second number (x). A second ENTER is not required because executing the operation terminates the second entry. In summary, to operate a two-argument function:
1. Enter the first (y) argument,
2. Press ENTER to terminate the first entry.
3. Enter the second (x) argument,
4. Execute the desired function.
When you link more than one operation, it is known as a chain calculation. A simple example is adding a list four numbers. Another example is adding two groups of numbers and then multiplying the two sums together.
In chain calculations, whatever in the display becomes the first argument of the operation. All that is needed is to enter the second argument (number), and then the required function. For chain calculations:
1. Enter the next required argument
2. Execute the desired function, no ENTER is required
The scope of this blog is just to give a very basic tutorial of RPL. It is a "do by example" tutorial. Keystrokes are shown in blue. All calculations on this blog are rounded to 4 decimal places.
This blog will demonstrate keystrokes on the 48S (works also on the 48SX), 48G (works also on the 48G+ and 48GX), and the 50g (works also on the 49g+).
==========================================================
To set the calculator to 4 decimal places:
HP 48S:
4 [ENTER] [LS] [CST] (MODES) [2nd soft key from left] (FIX)
HP 48G (via the Mode Selection Screen):
[LS] [MODES], choose Fix 4 on the menu
HP 50g (via the Mode Selection Screen):
[MODE], choose Fix 4 on the menu.
=========================================================
Examples: Calculating with RPL
Format of the display will be shown as follows:
[...]
[2: contents]
[1: contents]
Shift Keys
Left Shift [LS]: This key has an arrow going up and turning left. It is the third key up from the ON button on the left side. It is orange on the 48S, purple on the 48G, periwinkle on the 49G, green on the 49g+, and white on the 50g.
Right Shift [RS]: This key has an arrow going up and turning right. It is the second key up from the ON button on the right side. It is blue on the 48S, green on the 49G, light red on the 49G, red on the 49g+, and orange on the 50g.
The 28C has 1 shift key - in red.
Soft Keys: There are six soft keys on the top row of the keyboard. Their functions change depending on the current active menu. On the 48S and 48G series, these keys are not labeled. On the 49G, 49g+, and 50g, they are labeled F1 through F6, left to right. The soft keys are labeled as:
[F1] [F2] [F3] [F4] [F5] [F6]
In this tutorial I will put the label on the soft keys. [F1] mean the leftmost soft key, [F2] is the second leftmost key, and so on. Got it?
In this tutorial I will put the label of any shifted function or any function accessed by a soft key parenthesis after the key. For example, for the square function:
[LS] [ √ ] (x^2)
Press the left shift key, then the square root key. The square function is just labeled as the left-shifted function of that key.
Note: For the 50g, it is assumed that Soft Menus are turned on. (Flag -117 is set)
#1: 5 + 8
Keystrokes:
HP 48S/48G/50g: [ 5 ] [ENTER]
Display: [1: 5.0000]
HP 48S/48G/50g: [ 8 ] [ + ]
Display: [1: 13.0000]
Result: 13
#2: Chain Addition: 1000 + 1500+ 1750
Keystrokes:
HP 48S/48G/50g: 1000 [ENTER]
Display: [1: 1000.0000]
HP 48S/48G/50g: 1500 [ + ]
Display: [1: 2500.0000]
HP 48S/48G/50g: 1750 [ + ]
Display: [1: 4250.0000]
Result: 4,250
#3: To Clear the Stack
HP 48S: [LS] [backspace key]
HP 48G: [LS] [DEL]
HP 50g: [LS] [backspace key]
#4: 10 - 6
As in any calculation involving subtraction or division, the order of the arguments is important.
Keystrokes:
HP 48S/48G/50g: 10 [ENTER]
Display: [1: 10.0000]
HP 48S/48G/50g: 6 [ - ]
Display: [1: 4.0000]
Result: 4
#5: 6 x 2.95 + 2 x 1.28
Sometimes it is useful to leave previous results on the stack while working on parts of the problem. The order of operations tells us to do multiplication first, then addition.
HP 48S/48G/50g: 6 [ENTER] 2.95 [ x ]
Display:
[1: 17.7000]
Leave 17.7 on the stack for future use.
HP 48S/48G/50g: 2 [ENTER]
Display:
[2: 17.7000]
[1: 2.0000]
HP 48S/48G/50g: 1.28 [ x ]
Display:
[2: 17.7000]
[1: 2.5600]
Now complete the calculation.
HP 48S/48G/50g: [ + ]
Display:
[1: 20.2600]
Result: 20.26
# 6: 200 ÷ (3^2.5 - 1)
Keystrokes:
We'll start by entering 200 and leaving it on the stack for future use.
HP 48S/48G/50g: 200 [ENTER] 3 [ENTER]
Display:
[2: 200.0000]
[1: 3.0000]
HP 48S/48G/50g: 2.5 [y^x]
Display:
[2: 200.0000]
[1: 15.5885]
HP 48S/48G/50g: 1 [ - ]
Display:
[2: 200.0000]
[1: 14.5885]
We are ready for the division.
HP 48S/48G/50g: [ ÷ ]
Display:
[1: 13.7095]
Result: 13.7095
#7: 2 x (5 ^ 2.5 ÷ 2.5 ^ 5)
Take care of the fraction first, multiply it all by 2 in the end.
HP 48S/48G/50g: 2 [ENTER] 5 [ENTER]
Display:
[2: 2.0000]
[1: 5.0000]
HP 48S/48G/50g: 2.5 [y^x]
Display:
[2: 2.0000]
[1: 55.9017]
HP 48S/48G/50g: 2.5 [ENTER] 5 [y^x]
Display:
[3: 2.0000]
[2: 55.9017]
[1: 97.6563]
HP 48S/48G/50g: [ ÷ ]
Display:
[2: 2.0000]
[1: 0.5724]
Finish it off.
HP 48S/48G/50g: [ x ]
Display:
[1: 1.1449]
Result: 1.1449
# 8: 1/2 + 3/7 - √(25/64)
√ is the symbol for square root
Keystrokes (or one possible set of keystrokes):
HP 48S/48G/50g: 2 [1/x]
Display:
[1: 0.5000]
HP 48S/48G/50g: 3 [ENTER] 7 [ ÷ ]
Display:
[2: 0.5000]
[1: 0.4286]
HP 48S/48G/50g: [ + ] 25 [ENTER] 64 [ ÷ ]
Display:
[2: 0.9286]
[1: 0.3906]
HP 48S/48G/50g: [ √ ]
Display:
[2: 0.9286]
[1: 0.6250]
HP 48S/48G/50g: [ - ]
Display:
[1: 0.3036]
Result: 0.3036
#9: Find a decimal approximation, to four decimal places, of e^-3.
Keystrokes:
HP 48S: [ 3 ] [+/-] [LS] [1/x] (e^x)
HP 48G: [ 3 ] [+/-] [LS] [1/x] (e^x)
HP 50g: [ 3] [+/-] [LS] [y^x] (e^x) [RS] [ENTER] (->NUM)
Result: 0.0498
# 10: √(3^2 + 4^2)
Keystrokes:
HP 48S/48G/50g:
3 [LS] [ √ ] (x^2) 4 [LS] [ √ ] (x^2)
Display:
[2: 9.0000]
[1: 16.0000]
HP 48S/48G/50g:
[ + ] [√ ]
Display:
[1: 5.0000]
Result: 5
# 11: Find the percent change between 19.99 (old) and 34.99 (new)
%CHG = Δ% = [new - old] ÷ old x 100%
Keystrokes:
HP 48S:
19.99 [ENTER] 34.99 [MTH] [F1] (PARTS) [NXT] [F5] (%CH)
HP 48G:
19.99 [ENTER] 34.99 [MTH] [F5] (REAL) [F2] (%CH)
HP 50g:
19.99 [ENTER] 34.99 [LS] [SYMB] (MTH) [F5] (REAL) [F2] (%CH)
Result: 75.0375% change
Register Operations
Two common register operations are Swap and Roll Down.
Swap: This operation swaps the contents on the X and Y registers. The key is typically labeled [x<>y]. The swap function is useful when arguments need to be switched before performing subtraction, division, and taking powers.
# 12: 2 - (-5 x 3)
In order to demonstrate the Swap function, let's enter the multiplication first.
Keystrokes:
HP 48S/48G/50g:
5 [+/-] [ENTER] 3 [ x ]
Display:
[1: -15.000]
HP 48S/48G/50g:
2 [ENTER]
Display:
[2: -15.0000]
[1: 2.0000]
We need 2 on the top because we need to calculate 2 - (-5 x 3), not (-5 x 3) - 2. This is where the Swap operation comes in.
HP 48S/48G/50g:
[LS] [right arrow] (SWAP - not marked on the 50g+)
Display:
[2: 2.0000]
[1: -15.0000]
Now with the arguments in the proper order, we can execute the subtraction.
HP 48S/48G/50g:
[ - ]
Display:
[1: 17.0000]
Result: 17
# 13: Calculate 200 ÷ 40, but enter 40 first, then 200.
Here we can use the Swap operation to correct the order of dividend and divisor.
HP 48S/48G/50g:
40 [ENTER] 200
Display:
[1: 40.0000]
[ 200]
We need to swap the arguments.
HP 48S/48G/50g:
[ENTER] [LS] [left arrow]
Display:
[2: 200.0000]
[1: 40.0000]
Now we got it!
HP 48S/48G/50g:
[ ÷ ]
Display:
[1: 5.0000]
Result: 5
Roll Down: This operation pushes down the contents of the register one level. You choose how many of the levels "roll" down.
# 14 Roll down a three level stack.
A simple example: Say we have entered 4, 1, and 9 on to the stack and the stack is like this:
3: 4
2: 1
1: 9
((Clear Stack) 4 [ENTER] 1 [ENTER] 9 [ENTER])
I want to rotate the entire stack. The keystrokes for this is:
HP 48S:
[PRG] [F1] (STK) [F6] (DEPTH) [F4] (ROLLD)
HP 48G:
[LS] [up arrow] [F6] (DEPTH) [F4] (ROLLD)
HP 50g:
[LS] [EVAL] (PRG) [F1] (STACK) [NXT] [F6] (DEPTH) [F2] (ROLLD)
The stack looks like this:
3: 9
2: 4
1: 1
The Constant Pi (π)
The Pi key (or keystroke sequence) puts π on level 1 and lifts everything else one level.
# 15: Find the area of a circle with a radius of 2.35 inches.
Area = π *radius^2
Keystrokes:
HP 48S/48G/50g:
[LS] [SPC] (π) 2.35 [LS] [ √ ] (x^2) [ x ]
Display:
[1: 'π*5.5225']
HP 48S: [RS] [EVAL] (->NUM)
HP 48G: [LS] [EVAL] (->NUM)
HP 50g: [RS] [ENTER] (->NUM)
Display:
[1: 17.3494]
Result: 17.3494 square inches
Additional Examples
# 16: How many 5-card hands can be dealt out of a standard deck of 52 playing cards?
Combination = COMB = n! ÷ (k! x (n - k)!)
It is found in the Math-Probability Menu, labeled COMB
Keystrokes:
HP 48S:
52 [ENTER] 5 [MTH] [F2] (PROB) [F1] (COMB)
HP 48G:
52 [ENTER] 5 [MTH] [NXT] [F1] (PROB) [F1] (COMB)
HP 50g:
52 [ENTER] 5 [LS] [SYMB] (MTH) [NXT] [F1] (PROB) [F1] (COMB)
Result: 2,598,960 possible hands
# 17: You have purchased a calculator for $99.99 and present a coupon for 15% for the purchase price. Assume sales tax is 8.75%. What is the final amount due?
The percent function returns level 2 * level 1 ÷ 100 on level 1.
Keystrokes:
HP 48S:
99.99 [ENTER] [ENTER] 15 [MTH] [F1] (PARTS) [NXT] [F4] (%) [ - ] [ENTER] 8.75 [F4] (%) [ + ]
HP 48G:
99.99 [ENTER] [ENTER] 15 [MTH] [ F5 ] (REAL) [F1] (%) [- ] [ENTER] 8.75 [F1] (%) [ + ]
HP 50g:
99.99 [ENTER] [ENTER] 15 [LS] [SYMB] (MTH) [F5] (REAL) [F1] (%) [ -] [RS] [ENTER] (->NUM) [ENTER] 8.75 [F1] (%) [ + ]
Result: 92.4283 (The final bill is $92.43)
# 18: How to set the Angle Mode
HP 48S:
[LS] [CST] (MODES) [NXT] [NXT]
Select [F1] for Degrees, [F2] for Radians, [F3] for Gradients
HP 48G (via menu):
[RS] [CST] (MODES) [down arrow]
Use [F2] to choose the angle, press [F6] (OK) to accept the settings
HP 50g (via menu):
[MODE] [down arrow] [down arrow]
Use [F2] to choose the angle, press [F6] (OK) to accept the settings
# 19: While the calculator is in Radians mode, find sin^-1 (.5). Then convert the result to degrees.
See # 18 on how to set the calculator to Radians mode. Your calculator is in Radians mode if the display has a RAD indicator on the upper left corner of the screen.
HP 48S/48G/50g: .5 [LS] [SIN] (ASIN)
Display:
[1: 0.5236]
HP 48S: 180 [ x ] [LS] [SPC] (π) [ ÷ ] [RS] [EVAL]
HP 48G: [MTH] [F5] (REAL) [NXT] [NXT] [F6] (R->D)
HP 50g: [LS] [SYMB] (MTH) [F5] [NXT] [NXT] [F6] (R->D)
Display:
[1: 30.0000]
So sin^-1 (.5) ≈ .5236 radians = 30º
Note:
R->D is the Radians to Degrees function
D->R is the Degrees to Radians function
I hope you find this tutorial on RPL helpful.
Eddie
Wednesday, September 21, 2011
RPN Basics
(updated 9/25/2011)
This is a basic tutorial of reverse polish notation (RPN). RPN is an operating system that some calculators use, primarily those manufactured by Hewlett Packard. RPN removes the need to enter parenthesis during long calculations and allows for immediate feedback during calculations; you will not need to enter a long operation before getting feedback - thus eliminating errors. A lot of times, the number of keystrokes required to make a calculation is reduced using RPN compared to algebraic systems.
Typically, a RPN calculator uses a stack with four registers, named X, Y, Z, and T. Each register is stacked on top of another. A four-register stack diagram looks like this:
What is required of the user to execute a desired operation depends on the number of arguments (for our purpose, numbers) the function requires. Most scientific calculator functions require one or two arguments.
One-argument functions operate on whatever is in the display, or the X register. For one-argument functions, simply execute the desired operation. One-argument functions include all the trigonometric functions (sine, cosine, tangent), logarithms, exponential (e^), reciprocal, square root, and factorial (x!). The change sign operation fits under the category of one-number operations because it simply multiplies the number by -1. The change sign operation is often labeled either CHS (HP 12C, HP 15C) or +/- (HP 35S).
Two-argument functions operate on the contents on the Y and X registers. Common two-argument functions include the arithmetic operators (+, -, x, ÷), powers (y^x), combination and permutations, percent and percent change (Δ%). To use a two-argument function, enter the first number (y), then press ENTER. ENTER terminates the entry and gets the calculator ready to receive another number. Next, enter the second number (x). A second ENTER is not required because executing the operation terminates the second entry. In summary, to operate a two-argument function:
1. Enter the first (y) argument,
2. Press ENTER to terminate the first entry.
3. Enter the second (x) argument,
4. Execute the desired function.
When you link more than one operation, it is known as a chain calculation. A simple example is adding a list four numbers. Another example is adding two groups of numbers and then multiplying the two sums together.
In chain calculations, whatever in the display becomes the first argument of the operation. All that is needed is to enter the second argument (number), and then the required function. For chain calculations:
1. Enter the next required argument
2. Execute the desired function, no ENTER is required
A more detailed explanation of the stack can be found in manuals of the HP 12C, 15C, and 35S calculators. HP Website
The scope of this blog is just to give a very basic tutorial of RPN. A lot of examples are provided to illustrate how to use the functions on an RPN calculator.
Hewlett Packard:
Scientific: 15C (including Limited Edition), 35S, 48 Series, 32Sii, 41C, 50g+, and many others
Financial: 12C (all editions), 30b
iPod Apps:
GO-Sci 25, GO-Sci 21, just to name a couple.
You can look for RPN calculators online, many are available for the iPod, iPad, and Android operating mobile devices.
This tutorial is going to be a "do by example" tutorial. Keystrokes are shown in blue. All calculations on this blog are rounded to 4 decimal places.
* Note: This works for most models. In these examples, you may need to press a shift key to access an operation depending on the calculator. Since this tutorial covers a variety of calculators, the shift keys are omitted. Please check your manual.
#1: 5 + 8
Keystrokes:
5 [ENTER] Display: 5.0000
8 [ + ] Display: 13.0000
Result: 13
#2: 10 - 6
As in any calculation involving subtraction, the order is important.
Keystrokes:
10 [ENTER] Display: 10.0000
6 [ - ] Display: 4.0000
Result: 4
# 3: 6 x 2.95 + 2 x 1.28
Keystrokes:
6 [ENTER] Display: 6.0000
2.95 [ x ] Display: 17.7000
2 [ENTER] Display: 2.0000
1.28 [ x ] Display: 2.5600
Result: 20.26
# 4: 200 ÷ (3^2.5 - 1)
Keystrokes:
3 [ENTER] Display: 3.0000
2.5 [y^x] Display: 15.5885
1 [ - ] Display: 14.5885
Result: 13.7095
# 5: 1/2 + 3/7 - √(25/64)
√ is the symbol for square root
Keystrokes (or one possible set of keystrokes):
7 [ ÷ ] Display: 0.4286
[ + ] Display: 0.9286
64 [ ÷ ] Display: 0.3906
[ √ ] Display: 0.6250
[ - ] Display: 0.3036
Result: 0.3036
# 6: e^-3
Keystrokes:
3 [CHS] (or [+/-]) Display: -3
[e^x] Display: 0.0498
Result: 0.0498
# 7: √(3^2 + 4^2)
Keystrokes:
If a square operation [x^2] is available:
4 [x^2] Display: 16.0000
[ + ] Display: 25.0000
[ √ ] Display: 5.0000
If a [x^2] is not available:
4 [ENTER] 2 [y^x] Display: 16.0000
[ + ] Display: 25.0000
[ √ ] Display: 5.0000
Result: 5
# 8: Find the percent change between 19.99 (old) and 34.99 (new)
%CHG = Δ% = [new - old] ÷ old x 100%
Keystrokes:
If a percent change function [Δ%] is available:
34.99 [Δ%] Display: 75.0375
If [Δ%] is not available:
34.99 [ENTER] 19.99 [-] Display: 15.0000
19.99 [÷] Display: 0.7504
100 [x] Display: 75.0375
Result: The percent change is an increase of 75.0375%
Register Operations
Two common register operations are Swap and Roll Down.
Swap: This operation swaps the contents on the X and Y registers. The key is typically labeled [x<>y]. The swap function is useful when arguments need to be switched before performing subtraction, division, and taking powers.
#9: 2 - (-5 x 3)
Keystrokes:
5 [CHS] (or [+/-]) Display: -5
[ENTER] 3 [ x ] Display: -15.0000
2 Display: 2
[x<>y] Display: -15.0000
Result: 17
Roll Down: This operation pushes down the contents of the register one level.
In a four stack scheme:
Whatever was in the T register goes to the Z register
Whatever was in the Z register goes to the Y register
Whatever was in the Y register goes to the X register
Whatever was in the X register goes to the T register
The key often labeled R with a down arrow next to it. [R↓]
The Pi key (or keystroke sequence) puts π on the X register (display) and lifts everything else one level. On a four-register stack, whatever was held in the T register is lost.
#10: Find the area of a circle with a radius of 2.35 inches.
Area = π *radius^2
Keystrokes:
[π] Display: 3.1416
2.35 [x^2] [x] Display: 17.3494
Result: 17.3494 square inches
Alternatively: [ π ] 2.35 [ENTER] 2 [y^x] [ x ]
Additional Examples:
#11: How many 5-card hands can be dealt out of a standard deck of 52 playing cards?
Combination = n! ÷ (k! x (n - k)!)
This function has several labels: Cy,x (HP 15C), COMB (HP 42S, HP 50g+), or nCr (most calculators)
The factorial function has several labels, typically x! or n!.
Keystrokes:
If a combination function is available:
If a combination function is not available:
52 [ENTER] Display: 52.0000
5 [ - ] Display: 47.0000
[x!] Display: 2.5862 59 (2.5682 x 10^59)
[ x ] [1/x] Display: 3.2222 -62 (3.2222 x 10^-62)
52 [x!] Display: 8.0658 67 (8.0658 x 10^67)
[ x ] Display: 2,598,960.000
Result: 2,598,960 possible 5-card hands
#12: Find the sine of 30°
Keystrokes:
If necessary, set the calculator to degrees mode
30 [SIN]
Result: 0.5000
#13: You have purchased a calculator for $99.99 and present a coupon for 15% for the purchase price. Assume sales tax is 8.75%. What is the final amount due?
In RPN calculators, the percent function [ % ] returns Y * X%. The contents of the Y stack remain unchanged.
Keystrokes:
99.99 [ENTER] 15 [ % ] Display: 14.9985 (99.99 x 15%)
[ - ] Display: 84.9915
8.75 [ % ] Display: 7.4368 (84.9915 x 8.75%)
Result: 92.4283 (The final bill is $92.43)
#14: You deposit $1,000 in a bank account earning 3.5% interest for 5 years. How much money will you have after 5 years?
FV = PV x (1 + i%)^n
Where FV is the future value, PV is the present value, i is the periodic interest rate, and n is the number of periods. We are looking for FV with PV = 1,000, i = 3.5, and n = 5.
Keystrokes:
[ + ] Display: 1.0350
5 [ y^x ] Display: 1.1877
[ x ] Display: 1,187.6863
Result: 1,187.6863 ($1,187.68)
#15: On a right triangle, find the angle x in degrees:
/|
/ |
/ |
15 / |
/ |
/x |
--------
10
(my attempt at a right triangle, hopefully you get the picture)
x = arccos (10/15) = cos^-1 (10/15)
Keystrokes:
Set the calculator in Degrees mode if necessary.
[COS^-1] Display: 48.1897
Result: The angle is 48.1897°
I hope you find this tutorial on RPN helpful.
Eddie
Many thanks to Xavier A. and Dieter on the MoHPC (The Museum of HP Calculators) Forum.
Pictures of the HP 15C Limited Edition and the HP 12C 30th Year Anniversary Edition
HP 15C Limited Edition
The HP 15C Limited Edition is a reissue of the HP 15C that was in the market during the 1980s. The calculator had a horizontal interface. With the calculator operating in RPN (Reverse Polish Notation), users and fans of the HP 15C praised the calculator for ease of use and it's landscape shape. Features include: complex numbers, matrices, and keystroke programming up to 448 steps.
The 15C Limited Edition Scientific Calculator.
Monday, September 19, 2011
New Finds
Last week I bought two Hewlett Packard HP 15C limited Edition calculators. The limited edition is a reissue of the HP 15C calculator, a favorite of many scientists and mathematicians. I also bought a 30th Year edition of the HP 12C calculator, Hewlett Packard's best selling calculator for 30 years. I plan to post pictures soon, but if you want to buy one, check out www.HP.com, www.buy.com, Bach Company, or Samson Cables.
There is a lot of talk on the 15C on the Hewlett Packard Museum of Calculators forum ( http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/forum.cgi ). It is a forum for fans of math and Hewlett Packard calculators.
At the Azusa Swap Meet yesterday, I managed to pick up a TI-82 calculator. The TI-82 is basically the bridge between the TI-81 and the TI-83+/TI-84+ series. It is nice to fill holes in the collection.
Got to go, take care,
Eddie
Tuesday, September 13, 2011
Sharp EL-W516X Review
Hi everyone. Today I am giving a short review of the Sharp EL-W516X solar calculator. I bought this calculator at Target for $17.99.
The main features of the EL-W516X include: WriteView mode, statistical operations, matrix operations, base calculations, complex operations, and a drill mode. The drill mode tests your mathematical ability on arithmetic problems. While this mode has been panned, I find the drill mode enjoyable, and I challenge myself to see how fast I can correctly answer a set of questions.
Generally, this calculator is a remake of the Sharp EL-W516 calculator. A picture of both models are shown below, with the newer EL-W516X on the left, and the older EL-W516 on the right.
The set of operations of the EL-W516X is the same as the EL-W516. The normal mode allows you enter calculations in a linear format or a textbook format (WriteView ™). The textbook format reurns exact answers (fractions, fractions of π, square roots) whenever possible. Decimal equivalents can be accessed by pressing the CHANGE key (sometimes twice).
Some of them include:
Catalog. This calculator contains a catalog of all the functions available by pressing MATH, 0. The catalog is available in every mode.
Calculus. Functions include single variable numerical integration, single numberical derivatives, and the sum function (Σ). I am happy to report that on the several tests calculations I made with the EL-W516X, the calculator boasts a faster processor than its predecessor.
Statistics. Regressions include linear, quadratic, power, exponential, logarithmic, inverse, and general exponential (y = a * b^x). Normal distribution calculations are include in this mode. (finding the area but not inverse)
Base Operations.. The calculator offers five bases: decimal (standard), binary, octal, hexadecimal, and pental (base 5). To enter a base mode, all you Ned to do is to perform a conversion. To access the A-F in hexadecimal mode, you just need to press the corresponding key (no ALPHA key required). The logic operations (and, not, or, etc) are found in the catalog.
Equation Solving. In addition to the ability to solve any equation in one variable (X), the calculator has solvers for 2 x 2 and 3 x 3 linear systems, and the quadratic and cubic equation. The general solver is in form f(X) = 0, you supply the f(X).
Complex Mode. . This mode in my opinion, falls a little short. This mode can not use WriteView and it's operations are limited to polar/rectangular conversions, square (x^2), cube (x^3), and the arithmetic operations. I would have liked for it to do at least exponential and logarithms, as well as exponential powers beyond 3.
Definable Functions.. You can store up to four operations in memories D1 - D4 for later use. Not very useful because what you can store is limited.
Definable Formulas. You can store up to four formulas (including integrals, sums, and derivatives) in memories F1 - F4 for later use. I find this ability useful, you can store formulas for calculation or even for reference. The ALGB function (MATH, 1 in Normal Mode) can be used to substitute values for variables.
Other. The calculator offers basic matrix, lists, and table operations.
OVERALL
I like the sharp, crisp display of the EL-W516X. The calculator also has a faster processor - which means faster calculations (it pays truly pays off when doing numerical calculus). Function wise, this calculator has a lot to offer and us good pick up for anyone who wants an inexpensive calculator with a lot of function. 4 out 5 stars.
Wednesday, September 7, 2011
Ready for school?
Sorry I have not blogged in while. For the students: are you in school or about to go back? What math classes are you taking?
Sunday, June 26, 2011
Texas Instruments TI-nspire CX Short Review
The CX boasts a color screen. You are able to edit certain text (in the Notes Application), graphs, and cells in 15 colors. The color screen has a better contrast to their black and white nspire counterparts. The best part is that I can read the screen anywhere at any angle instead of having to tilt my calculator to certain degrees.
The CX has a much better keyboard than the Touchpad. I won't go into how much dislike users have for the original Clickpad here, but the alphabetic keys on the bottom of the Touchpad were atrocious. The keys were hard to press, put a lot of pressure on the finger, and the keys put a strain on my hands after typing on it for several minutes. Thankfully, TI corrected this problem and on the CX the alphabetic keys on the bottom of the unit have a more tactile feel to them. The keys are easy to press.
Although, what is up with the trigonometric functions not being on the keyboard? Same for π and θ.
The CX also has 100 MB of memory - which is a lot for a calculator. It may not be the biggest, because an HP 50g calculator can have up to 4 GB(?) on it with the use of an SD card, but that is a ton of memory for a calculator noneoftheless.
The CX package comes with the Student Software. The Software can be used to emulate the nspire CX and also act as the link between the calculator and the computer.
Overall, I enjoy using the nspire CX and can not wait to get my hands on the CAS version.
TI nspire webpage
Saturday, June 4, 2011
My Favorite Number
Even though I am a fan of numbers in general, my favorite number is π. π is the famous irrational constant used in measuring the area and circumference in circles, plays an important role in trigonometry, and the Gamma of 1/2 is the square root of π. Every March 14 is designated π Day, celebrated around the world, particularly in mathematical circles, schools, and universities. It also happens to be the birthday of Albert Einstein, Billy Crystal, Les Brown, Quincy Jones, and yours truly (Eddie - the writer on this blog).
Going by memory, the first 15 digits of π is 3.14159 26535 89793.
So, what is your favorite number?
Tuesday, May 24, 2011
Polynomial Derivative and Integral for HP 35S
This program calculates the coefficients of the derivative and the integral of a polynomial. The maximum degree of the polynomial can be is seven.
The variables of the polynomial are:
H x^7 + G x^6 + F x^5 + E x^4 + D x^3 + C x^2 + B x + A
Instructions:
1. Load the Polynomial. Press XEQ P001, enter the degree of the polynomial and load the coefficients from the highest degree to the constant.
2. Operation. To find the derivative, press XEQ P033. For an indefinite integral, press XEQ P083.
Program
' Start of program
' Messages in quotes can be typed by pressing the EQN key. Each letter is typed as so: RCL letter .
' To set/clear flag 10 press Gold Shift FLAGS. 1 for Set, 2 for Clear. "Type" 10 by pressing the decimal point followed by the zero.
P001 LBL P
P002 SF 10
P003 "DEGREE"
P004 PSE
P005 CF 10
P006 INPUT N
P007 1
P008 +
P009 STO M
P010 SF 10
P011 "X^"
P012 PSE
P013 RCL M
P014 1
P015 -
P016 PSE
P017 1
P018 +
P019 +/-
P020 STO I
P021 "COEF"
P022 PSE
P023 CF 10
P024 RCL(I)
P025 STOP
' STOP is entered by pressing R/S
P026 STO(I)
P027 DSE M
P028 GTO P010
P029 SF 10
P030 "DONE"
P031 CF 10
P032 RTN
' Derivative Routine
P033 1
P034 RCL+ N
P035 STO M
' Calculate the coefficients
P036 RCL M
P037 +/-
P038 STO I
P039 +/-
P040 -1
P041 RCL+ M
P042 STOx(I)
P043 DSE M
P044 GTO P036
' Shift the coefficients to the appropriate slots
P045 2
P046 1
P047 RCL+ N
P048 1000
P049 ÷
P050 +
P051 STO M
P052 RCL M
P053 IP
P054 +/-
P055 STO I
P056 RCL(I)
P057 1
P058 STO+ I
P059 R↓
P060 STO(I)
P061 ISG M
P062 GTO P052
P063 RCL N
P064 +/-
P065 1
P066 -
P067 STO I
P068 0
P069 STO(I)
' Display Routine
P070 RCL N
P071 STO M
P072 RCL M
P073 +/-
P074 STO I
P075 VIEW(I)
P076 DSE M
P077 GTO P072
P078 SF 10
P079 "DONE"
P080 PSE
P081 CF 10
P082 RTN
' Integral Routine
' Calculate the coefficients
P083 1
P084 RCL +N
P085 STO M
P086 RCL M
P087 +/-
P088 STO I
P089 +/-
P090 1/x
P091 STOx(I)
P092 DSE M
P093 GTO P086
' Shift the coefficients into the proper place
' The constant term is assigned 0 (technically, it is an arbitrary constant)
P094 1
P095 RCL+ N
P096 STO M
P097 RCL M
P098 +/-
P099 STO I
P100 1
P101 -
P102 RCL(I)
P103 x<>y
P104 STO I
P105 x<>y
P106 STO(I)
P107 DSE M
P108 GTO P097
P109 0
P110 STO A
' Display Routine
P111 RCL N
P112 2
P113 +
P114 STO M
P115 RCL M
P116 +/-
P117 STO I
P118 VIEW(I)
P119 DSE M
P120 GTO P115
P121 SF 10
P122 "DONE"
P123 PSE
P124 CF 10
P125 RTN
' End of Program
Memory: LN=433
Example
Find the derivative and integral of f(x) = x^3 - 2x^2 + 1
Derivative:
1. XEQ P001
2. Enter 3 at DEGREE prompt, then press R/S
3. "X^3" : 1, R/S
4. "X^2" : -2, R/S
5. "X^1" : 0, R/S
6. "X^0" : 1, R/S
7. XEQ P033. Press R/S after each coefficient.
Then f'(x) = 3x^2 - 4x
For the integral:
1. XEQ P001
2. Enter 3 at DEGREE prompt, then press R/S
3. "X^3" : 1, R/S
4. "X^2" : -2, R/S
5. "X^1" : 0, R/S
6. "X^0" : 1, R/S
7. Press XEQ P083.
Then the integral is .25x^4 - .6666666667x^3 + x
Recall that the variables of the polynomial are:
H x^7 + G x^6 + F x^5 + E x^4 + D x^3 + C x^2 + B x + A
Sunday, May 15, 2011
Complex Number Operations (Part II)
For all the calculations, let z = a + bi
Assume your calculator is in Radians Mode. The algorithms are suggested.
Exponential of a Complex Number
e^z = e^a (cos b + i sin b)
This calculation is fairly easy because it is relatively straight forward.
A sample RPN (Reverse Polish Notation) routine would look like:
With b on the y stack and a on the x stack:
e^x
STO 0 (or whatever register or variable you want as temporary storage)
x< >y (swap)
ENTER
SIN
RCL 0
×
R↓
COS
×
x< >y (swap)
R↓
Result: real(e^z) is on the x stack, while imag(e^z) is on the y stack
Natural Logarithm of a Complex Number
ln z = ln r + i θ
where r = √(x^2 + y^2) and θ = arctan(y/x)
Casio fx-115ES:
ln(abs(a + bi)) + i arg(a + bi)
Sharp EL-W516:
ln(abs(a + bi)) + i tan^-1(b÷a)
TI-36X Pro:
ln(abs(a + bi)) + i angle(a + bi)
With b on the y stack and a on the x stack, a sample RPN routine mat look like this:
→P (Rectangular to Polar conversion)
LN
Argument vs Arctangent (tan^-1)
Bear in mind that the argument (often labeled arg or angle for TI calulators) and the arctangent functions returns different angles. However the angles are accurate, recall the identity tan(x ± π) = tan(x).
Ranges of Calculator Functions:
angle/arg returns the angle between -π/2 and π/2 (-90° and 90°)
tan^-1 returns the angle between 0 and π (0° and 180°)
Sine of a Complex Number
There are two general formulas to calculate the sine of a complex number
(1) sin z = sin a cosh b + i cos a sinh b
(2) sin z = (e^iz - e^-iz)/(2i)
Formula (2) is good if your calculator can handle e^z. For the non-graphing calculators, I recommend using formula (1).
A sample RPN routine looks like this:
With b on the y stack and a on the x stack:
STO 0 (or A)
COS
x< >y
STO 1 (or B)
SINH
×
RCL 1 (or B)
COSH
RCL 0 (or A)
SIN
×
Cosine of a Complex Number
Calculating the cosine of a complex number is similar:
(1) cos z = cos a cosh b - i sin a sinh b
(2) cos z = (e^iz + e^-iz)/2
A sample RPN routine looks like this:
With b on the y stack and a on the x stack:
STO 0 (or A)
SIN
CHS (+/-)
x< >y
STO 1 (or B)
SINH
×
RCL 1 (or B)
COSH
RCL 0 (or A)
COS
×
The formulas are presented for completion.
ArcSine and ArcCosine
These formulas are presented for completion.
sin^-1 z = -i ln( i z ± √(1 - z^2))
cos^-1 z = -i ln(z ± i√(1 - z^2))
The principle angle is given by using +.
(staff.jccc.net)
Complex Power of a Complex Number
Let z and w be complex numbers, then:
z^w = e^(w ln z)
(HP 41C Math Pac)
Sunday, May 8, 2011
Complex Number Operations
Introduction
Complex numbers have been a recurring feature on scientific calculators, and for most calculators, the calculations we can readily do on them have been limited - particularly on non-graphing scientific calculators.
If your non graphing calculator has complex number calculations, chances are this is the limit of what the calculator can do:
* Arithmetic (+, -, x, ÷)
* Square, but not square root
* Cube, but not cube root
* Rectangular/Polar conversions
* A separate function for magnitude, angle, real, and imaginary part extraction
The point of this blog is to give you some tricks to extend the calculation of complex numbers:
* Powers and principal root
* Exponential and Natural Logarithm (next week)
* Sine and Cosine (next week)
For any calculators using reverse polish notation (RPN), such the HP 35S, HP 50g, HP 15c, or even apps such as the GO-25 SCI RPN; I will present a "generalized" routine that you can use to perform the calculations. Please adjust as necessary what how your calculator works best.
Sources:
HP 41C Math Pac, Hewlett Packard, 1979
Square of a Complex Number
By simple algebra, we can calculate the square of a complex number as:
(a + bi)^2 = (a^2 - b^2) + 2abi
Remember that i = √-1, so i^2 = -1.
Thankfully, scientific calculators allow this calculation simply by typing in (a + bi)^2.
For calculators using RPN, try this routine: starting with b stored in Register 2 (or letter if you have a HP 35S, 48, 50g...family) and a stored in Register 1
RCL 2
RCL 1
X
2
X (imaginary part)
RCL 1
2
y^x
RCL 2
2
y^x
- (real part)
Power (and Principal Root) of a Complex Number
By De Moive's Theorem, we can calculate the power of any complex number as:
(a + bi)^n = r^n (cos (nθ) + i sin (nθ))
Where: r = a^2 + b^2, θ = arctan (b/a), and n is a real number
Note abs(a + bi) = r and arg(a + bi) = θ (arg is named angle in the TI calculators)
On calculators such as the Casio fx-115ES, TI-36X Pro, and the Sharp EL-W516; unless n = 2 or n = 3, straight input will cause an error message. Use the above formula as the alternate. The nice thing of both the fx-115 and the TI-36X Pro is that we can store complex numbers to variables.
So the key strokes for the fx-115ES would look somewhat like this:
MODE 2
a + bi SHIFT STO A
Then input:
Abs(A)^(n) × (cos(n arg(A))+ i sin(n arg(A)))
For the TI-36X Pro:
a + bi sto→x [x y t z a b c d key]
Then input:
Abs(A)^(n) × (cos(n angle(A))+ i sin(n angle(A)))
For the EL-W516, complex numbers cannot be stored to variables. In addition, there is angle/argument function.
MODE 3
abs(a + bi)^n × (cos(n tan^-1(b ÷ a)) + i sin(n tan^-1(b ÷ a)))
A Sample RPN Routine for (a + bi)^n
Let a be stored in Register 1
Let b be stored in Register 2
Let n be stored in Register 3
RCL 2
RCL 1
→P
RCL 3
y^x
STO 0. (temporary register)
x<>y
RCL 3
×
Enter
SIN
RCL 0
×
x<>y
COS
RCL 0
×
Wednesday, April 27, 2011
TI-36X Pro Review
TI-36X Pro Review
This is a review of the TI-36X Pro Calculator by Texas Instruments.
History
Originally, this was the TI-30X Pro that was sold in Europe during the Autumn of 2010. Unfortunately, the 30X Pro had many bugs and as a result Texas Instruments quickly pulled the calculator off the market.
Click on this link for an article on the TI30X_Pro . The datamath.org website, which has this article, is maintained and run by Joerg Woerner, is an excellent site for Texas Instruments calculators, past and present.
Recently, Texas Instruments released the TI-36X Pro, based on the TI-30X Pro; thankfully without the bugs. I got this calculator on 4/25/2011 at an Office Depot store in West Covina, California (greater Los Angeles area).
What the 36X Pro Does
The TI-36X Pro is Texas Instruments answer to Casio's fx-115 ES and Sharp's EL-W516 calculators. The calculator is dual powered - solar for operation and battery for memory retention. The 36X-Pro is designed to allow user to enter expressions exactly the way they are normally written. Exponents have a superscript, fraction bars can contain expressions, and answers can be shown in fraction form, decimal form, and if applicable, radical form or coefficients of π.
The 36X-Pro welcomes a return of the definite integral, something that has been missing on TI non-graphing calculators since the TI-68 (we are talking the late 1980s). In addition, the 36X-Pro adds the numerical derivative, sums (Σ), and products (Π).
Although the 36X-Pro enjoys a TI-84+ interface, the calculator features buttons that cycle through a list of functions with repeated presses of a button. They are:
ln log button: ln, log, log to any base
e 10 button: e^ (exponential function), 10^
π e ι button: the constant pi, the constant e, √-1 (for working with complex numbers)
sin button: sin, sin^-1, sinh, sinh^-1
(cos and tan buttons work similarly)
! nPr nCr button: factorial (integers only), permutations, combinations
The variable button works the same way, cycling through eight variables (an ALPHA key would SO much better). Thankfully, all the calculus functions require that x be the dummy variable, requiring only one press of the variable button.
Sadly the percent function still doesn't "work". All it does is divide the number attached to the % by 100. Hence typing 21.99 + 9.75% returns 22.0875, not 24.134025 (what it should be).
The 36X-Pro is function rich: prime factorization, fraction and integer extraction, absolute value, polar to rectangular conversions and vice versa, modulus, basic matrix operations, basic vector operations, base n conversions, logic functions, and random numbers. For statistical regressions, you are not limited to linear. Quadratic, Cubic, Logarithmic, Power, and Exponential are available. A trend that I am also seeing in non-graphing scientific (and financial) calculators is that distribution calculations are offered. For the 36X-Pro, this includes the Normal distribution and inverse (from a lower tail area), and discrete distributions Poisson and Binomial.
The numeric solver on the 36X-Pro works pretty quickly for most equations. You do not have to set each equation equal to zero, the calculator allows you to enter the equation as is. You also get 2 and 3 systems of equations. A cool feature of the simultaneous solver is that if the calculator will let you know if the system has no solutions or infinite solutions For the 3x3 case, equations for which solutions cam be found. Example: x = -168/11 + 12z, y = 72/11 - 4z, z = z.
The polynomial solver works with quadratic and cubic equations.
The 36X-Pro has one OP function that you can store simple macros. The macro takes one number as input. You can store the final result (only the final result) into a variable. The OP is good for quick functions and one-step recurrence relations. It won't do multiple step functions, loops, or comparisons. Examples of macros include "*2+3" and "+x→x". There is also an expr-eval (evaluate expression) function that you can temporarily store an expression with variables, including calculus functions (x is the dummy variable). Be aware that the evaluation function works one time. There is also a table mode, but the expression is in terms of x, so the table feature is not good for sums (Σ), integrals, or derivatives.
As far as complex number calculations are concerned, you are limited to arithmetic, square, cube, reciprocal, absolute value, angle, real and imaginary part extraction. The nice thing is that you can evaluate more complex functions with complex numbers...if you know the formulas.
The 36X-Pro has 20 common conversions (English-Metric, Temperature, Speed, Length, Pressure, Power, Electricity) and 20 common physical constants in SI units. (meter-kilogram-second system)
What I Like
* This is the most advanced non-programmable Texas Instruments scientific calculator since the TI-68, and it's solar!
* The operation is integrated: you do not have to switch to a separate matrix mode, complex mode, vector mode etc, to take advantage of these functions. This is my one big gripe about the Casio fx-115ES.
* I like the multiple touch keys - they clean up the keyboard (see exception below)
What I am not crazy about
* Only one key to access eight variables. To get the variable a, you have to press the variable key FIVE times. Yikes! TI was better off making an Alpha key and assign an alphabetical variable (and possibly θ) to each key.
* The arithmetic keys are chrome on silver - if it were not for the etchings, I would not be able to see the arithmetic symbols.
* Limited complex number functions. However, it is common that complex number functions on a calculator are usually limited.
Worth the buy?
I say yes. The 36X-Pro is a nice calculator and well designed. I say it is comparable to the Casio fx-115ES and Sharp EL-W506 both in terms of speed and overall functionality. For the time being, the 36X-Pro is offered in select stores, but I suspect that within a few months this calculator will be everywhere competing with the fx-115ES for shelf space in stores everywhere. I paid $21.99 for it.
Calculator Forensics: 9.000001562
What's in the Package
* TI-36X Pro Calculator with hard case and quick reference card
* A detailed and sturdy pocket manual. You can download the manual online from TI's website.
Happy Calculating!
Texas Instrument's TI-36X_Pro_Page
Wednesday, April 20, 2011
HP 10bii+ Review
This is the review of the Hewlett Packard HP 10bii+ financial calculator.
The HP 10bii+ is a substantial upgrade to the HP 10bii. Hewlett Packard finally utilized the keyboard to its fullest, adding many functions such as depreciation, probability distribution calculations, bonds, expanded statistic capabilities, and depreciation just to name a few.
For this review, I have worked out all the examples prescribed in the manual provided. I also worked some of the examples with other finance calculators (10bii, 12c, 17bii+, 30b) just to see if the calculators have consistent answers. I am happy to report that the 10bii+ is consistent with the other financial calculators.
As for speed, I would state from the testing I did so far, the speed of the 10bii+ is pretty much on par with the 12c (two-battery edition) and the 30b.
The Keyboard
The colors on the keyboard are nicer and brighter than its predecessors. I can actually see the blue shifted functions in all levels of light and angles. The keys are tactile and easy to push. No missed keystrokes during normal operation.
Thankfully, the HP 10bii+ it can take a spill and clean up easily, and no, I did not plan that. I was able to clean the calculator immediately and it works in perfect order.
Memory
The 10bii+ sports 20 memory registers: 0 through 9 and .0 through .9. Store arithmetic is provided, but not recall arithmetic. There is a dedicated M register with three keys dedicated to it: →M (store to M), RM, and M+. I really like this feature, which allows me to calculate a sum of a large amount of numbers. The M register has been a feature on the 10b series since the beginning.
The memory allocation for cash flows and data points are as follows:
* Up to 45 cash flows can be stored.
* Up to 45 data points can be stored - if you want the full statistical features of the 10bii+.
There is a catch though. The 10bii+ allows space dedicated for 15 cash flows and 15 data points. There are 30 slots that are shared between cash flows and data points. Once the slots are filled, and you will no longer be able to store cash flows. However, the manual states that you can continue to add data points at a cost: you can no longer review data points and the only have linear regression available. More on cash flows and statistics later.
One nit picky point, the STO function is still a shifted function (orange). Personally, I like STO to be a primary function (unshifted), but no big deal.
You can also recall mostly anything by first pressing RCL then the variable or storage register you want.
Mathematics
With the new 10bii+, you gain a ton of new mathematics functions:
* The constant π = 3.141592653589793...
* Trigonometric functions: sine, cosine, tangent and their inverses. Just remember if you want inverses, activate INV first (blue shift, M+ key)
* Hyperbolic functions and their inverses
* Permutations and Combinations
* The factorial function now serves ALL real numbers from -252.999999999 (nine 9s) to 253.119. I like this a lot, became the gamma function is one my favorite functions. Γ(x) = (x - 1)!
* Random Numbers from 0 to 1.
* Radian and Degree modes, but not angle conversions.
Calculator Forensics asin(acos(atan(tan(cos(sin(9))))))
Degree Mode: 8.99999864267
Chain or Algebraic
The 10bii+ offers to operating modes: Chain or Algebraic. Chain mode is obvious: any operations act immediately on the displayed number. Order of operations are ignored. The Algebraic mode is not of the "enter the entire expression and then press enter" type. For one argument functions, enter the number first then press the function.
Example:
2 ln(12.5) + sin(30°) would require the key presses
2 x 12.5 [orange shift] [2 key for LN] + 30 [blue shift] [÷ key for SIN] =
(answer 5.55145728862)
I wish HP would have implement RPN (Reverse Polish Notation) mode - even if the mode just turned the left and right parenthesis into swap the x and y registers (x<>y) and roll the stack down one level (R↓), respectively.
Last Answer... and a Bug?
The 10bii+ offers a last answer feature, which is new to the 10b series. The last answer is what was in the display when the equals key (or any key that finishes an operation, I think) was last pressed. The last answer can be accessed by pressing RCL =.
But there is a bug. While working the example on page 41 of the manual:
Here is how it was presented in the manual:
50 INPUT (Display: 50)
22 + 14 [orange shift] [% key for %CHG] (Display: -28. last answer is supposed to have 36)
60 INPUT (Display: 60)
RCL = (Here the display is supposed to say 36, but I get 60 instead)
[orange shift] [% key for %CHG] (Display is supposed to say -40, instead I get 0)
My guess is that pressing INPUT also loads the displayed number in the last answer register.
Two Ways to Operate Two Argument Commands
The 10bii+ presents two ways to work with two argument commands: use of the INPUT, and the direct, "in-line" way.
The INPUT way is the classic way in the 10b series: number or operations, INPUT key, number or operations, function key(s).
The direct way is: number, function key(s), number, = key. Personally, I prefer this method - more straight forward.
You get the option with: combination, permutation, Student's t Distribution functions, percent change, DATE function, days between dates function.
Time Value of Money
The time value of money keys on the 10bii+ work (nearly) exactly like the time value of money keys work on any other HP calculator. The interest key (I/YR) works with annual interest rate (the 12c series work with the periodic interest rate). Solving time value of money problems are straight forward: enter the known amounts, press the variable to be solved for by just pressing the key. No compute key necessary.
For those of you new to HP financial calculators, Chapter 5: Picturing Financial Problems and Chapter 6: Time Value of Money on the full manual provide an excellent introduction and a good set of practice problems regarding time value of money.
New: a dedicated clear time value of money function. No more C ALL required - nice!
Profit Calculations
Calculations regarding cost, price, margin, and markup follow the model of the time value of money application. Enter the known information, then press the key of the desired variable to solve for it.
Cash Flows
At first glance, it looks like the cash flow application was untouched. Not so. This application is updated - BIG TIME.
First we get not one, but two ways of entering repeated cash flows:
The classic way:
Cash flow, CFj key, frequency, [orange shift], [CFj key for Nj]....
And the INPUT way, which I am a fan of:
Cash flow, INPUT key, frequency, CFj key
Next, like the time value of money registers, there is an all important clear cash flows sequence.
Third, when net present value (NPV) is calculated, you also calculate net future value (NFV). NFV is accessed by the SWAP function after NPV is calculated.
Finally, we can now review cash flows and their frequencies. This is done by simply pressing RCL CFj. Cash flows and frequencies can be reviewed, added, inserted, and deleted.
Date Calculations
One of my favorite calculator features have finally made it to the 10bii+: date functions! Dates can be entered in U.S. Format (mm.ddyyyy) and International Format (dd.mmyyyy). Two functions are available: Days between Dates and Date Addition. For example, if today is April 21, 2011 - then I am alive a grand total of 12,456 days. :)
Bonds
If you are familiar with the bond functions on the 12c, them you should at home with the 10bii+. There are separate storage registers for Settlement Date, Maturity Date, Coupon Rate, and Call Amount. You can calculate the price of the bond, yield to maturity, and the accrued interest. With many dedicated keys to bonds, you can keep track of what each variable contains.
Breakeven
The breakeven application is similar to the time value of money application. Enter amounts for the known variables then solve for the ones you want.
Depreciation
Straight Line, Sum of the Years Digits, and Declining Balance are available. Too bad declining balance with crossover is not (for calculating depreciation for tax purposes). The depreciation functions use the time value of money variables:
N for number of periods
I/Y for declining rate (if applicable)
PV for cost
FV for salvage value
The depreciation functions calculate the year's depreciation, and the remaining book value. The functions only work in whole years - meaning you will not be able to set up the first month. If you want to work with non-integers (say the asset has 5 1/2 years), you can calculate the first five years, but the calculating the sixth year returns 0. A possible work around in this Case is to use the remaining book value from year 5 as the 6th (and final) year of depreciation.
Statistics and Distributions
The statistics application is similar to the cash flow application. You can review entries and edit them, there is a clear data points sequence, and you can easily find the most common statistics measurements (mean, deviation, sums).
I was surprised to find that the 10bii+ has six regressions:
1. Linear, y = m x + b
2. Logarithmic, y = m ln x + b
3. Exponential, y = b exp(m x)
4. Power, y = b x^m
5. Exponent, y = b m^x
6. Inverse, y = m/x + b
The variables m, b, and the correlation coefficient (r) can be found by pressing the orange shift, the appropriate key, the orange shift key again, and then swap. The 10bii+ also features best fit (Regression 0). However, to find which regression fit the data points better, you will have to attempt to either predict x or y, or calculate a weighted average. One thing that can be improved is that the 10bii+ actually stating the best fit when it is activated.
The 10bii+ also has lower tail normal distribution and Student's t distribution CDF function and their inverses. I think labeling the distribution functions LTND (lower tail normal distribution) and Student (lower tail student's distribution) may have been better than z <>p and df,t <> p , respectively. But it works, and works well.
What's Impressive
* A well written full manual, which is available on CD or online. Now if the writers finish the last example in Chapter 13...
* The ability to review and edit cash flows and data points.
* Distribution functions and the fact that the factorial function coves real numbers
* Date functions, bonds, and depreciation have been added
* Unlike the 30b, you don't have to dig through menus to find functions, everything for the most part is on the keyboard
Wish List
* RPN mode
* When best fit mode is activated, you are told what regression model is selected without having to calculate a prediction first
* A better case, something similar to the one used for the 17bii+
* A "K" indicator when the constant function is used
Manual Curiosities
This covers Edition 1
* Page 41: RCL = does not work (well) after pressing INPUT
* Page 119: the paragraph comparing standard deviation and population deviation is repeated four times on this page
* Page 154: net future value example is not complete
Recommendation
I would recommend purchasing the 10bii+. It is a very solid calculator good for the entry level while having a lot of easy to use finance applications. Hewlett Packard has stepped up their game by updating the 10b series.
Great work, Hewlett Packard!
Hewlett_Packard's_HP_10bii+_Page