(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)

A blog is that is all about mathematics and calculators, two of my passions in life.

## 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

**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.

**Calculators with RPN**

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.

**Examples: Calculating with RPN**

#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

**[ + ]**Display: 20.2600

Result: 20.26

# 4: 200 ÷ (3^2.5 - 1)

Keystrokes:

**200 [ENTER]**Display: 200.0000

**3 [ENTER]**Display: 3.0000

**2.5 [y^x]**Display: 15.5885

**1 [ - ]**Display: 14.5885

**[ ÷ ]**Display: 13.7095

Result: 13.7095

# 5: 1/2 + 3/7 - √(25/64)

√ is the symbol for square root

Keystrokes (or one possible set of keystrokes):

**2 [1/x]**Display: 0.5000

**3 [ENTER]**Display: 3.0000

**7 [ ÷ ]**Display: 0.4286

**[ + ]**Display: 0.9286

**25 [ENTER]**Display: 25.0000

**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:

**3 [x^2]**Display: 9.0000

**4 [x^2]**Display: 16.0000

**[ + ]**Display: 25.0000

**[ √ ]**Display: 5.0000

If a [x^2] is not available:

**3 [ENTER] 2 [y^x]**Display: 9.0000

**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:

**19.99 [ENTER]**Display: 19.9900

**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

**[ - ]**Display: 17.0000

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 Constant Pi (π)**

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:

**52 [ENTER] 5 [nCr]**

If a combination function is not available:

**5 [x!]**Display: 120.0000

**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%)

**[ + ]**Display: 92.4283

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:

**1000 [ENTER] 1 [ENTER] 3.5 [ % ]**Display: 0.0350

**[ + ]**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.

**10 [ENTER] 15 [ ÷ ]**Display: 0.6667

**[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 box.

The 15C Limited Edition Scientific Calculator.

The 15C came with a written manual, which is probably a copy of the original 15C manual, a carrying case, and something really nice: a 15C emulator. I have yet to try the emulator but it is on the list of things to do. I am real excited to get the 15C Limited Edition. The new 15C is 100 times faster than the original model released in the 1980s. The Limited Edition is the first time in over 20 years that 15C calculators were produced. I understand that there are originally 10,000 calculators produced - hopefully more will be in the future. So if you want one, get shopping immediately!

**HP 12C 30th Year Anniversary Edition**

## 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?

### Σ(1 / (a^n)) from n=1 to m

Σ(1 / (a^n)) from n=1 to m This blog entry covers the sum of the series: Σ[1 / (a^n), n=1 to m] with n and m positive integers Specific Cas...