Retro Review: Casio fx-85WA

Retro Review: Casio fx-85WA

I want to give a special thank you to John Cadick. Cadick requested that I review this calculator and has loaned me his calculator to review. Much appreciated, and John, I hope you like this review.

General Information

Company: Casio

Type: Scientific – Algebraic (Perfect Algebraic Method)

Display: 10 digits with 2 digit exponents

Power: Solar with battery backup (LR44)

Memory Registers: 8: A, B, C, D, E, F, X, Y ,M

Years: Circa 1998-1999

Original Cost: $10 to $20, depending on the store (at the time)

Documentation: Manual, Quick Reference card

Two Line Display and Fractions

The Casio fx-85WA has a two line display: the top line for the mathematical expression to be evaluated, and the bottom line displays the answers. The font on the bottom line is bigger than the font on the top line. Later models will have the fonts of both lines of about equal size.

Screen for fx-85WAS (left) and FX-300MS (right)

You can enter equations as they are written, no need to worry about post-fix notation. The order of operations is effect for all calculations.

You can enter and do calculations with fractions with the [ a b/c ] key. After a calculation is completed, the [ a b/c ] can convert results between a fraction and decimal approximation. All fractions are simplified. The maximum denominator is 9999. Conversions between mixed fractions and improper fractions are also available.

The functions available are:

* Trigonometry: sine, cosine, tangent, with inverse and hyperbolic

* Logarithmic: natural and common, with inverses

* Square, square root, cube, and cube root (all primary key functions on the fx-85WA)

* Reciprocal, factorial (calculating 69! on the fx-85WS is surprising slightly faster than later models)

* Combination, permutation

* Engineering notation with the [ENG] and its inverse

* Degree-Minute-Seconds calculations [ ° ‘ “ ] and conversions

* Fractions, random numbers, round result to the FIX settings

* Polar and Rectangular Conversions

For the polar and rectangular conversions, results are stored in the following variables:

E: x, r

F: y, θ

Replay

The last expression can be edited. To re-edit the last expression, simply press either the arrow keys [ ← ] or [ → ] and edit. Characters can be inserted and deleted.

Statistics

There are two primary statistics modes on the fx-85WA:

* SD (Single Deviation, 1-variable statistics)

* REG (Regression, 2-variable statistics)

The type of regressions are:

Lin: Linear (y = a + b*x)

Log: Logarithmic (y = a + b*ln x)

Exp: Exponential (y = a + b*e^x)

Pwr: Power (y = a*x^b)

Inv: Inverse (y = a + b/x)

Quad: Quadratic (y = a + b*x + c*x^2)

Data points are entered with the [ M+ ] key with frequencies added with the semicolon ( ; ). When data is entered, the x value is returned. There is no data count indicator when [ M+ ] is pressed, I wish it did. Keep this in mind.

All the statistics registers are kept as shifted functions and alpha registers, and they are:

SHIFT 1: mean x	SHIFT 6: sy*	RCL A: ∑x^2	RCL F: ∑xy
SHIFT 2: σx	SHIFT 7: A (intercept)	RCL B: ∑x	RCL M: ∑x^3
SHIFT 3: sx*	SHIFT 8: B (slope, x coef.)	RCL C: n	RCL X: ∑x^2y
SHIFT 4: mean y	SHIFT 9: C (x^2 coef.)	RCL D: ∑y^2	RCL Y: ∑x^4
SHIFT 5: σy	SHIFT (: r (correlation)	RCL E: ∑y

* labeled xσn-1 and yσn-1, respectively. (sample deviation)

Keyboard

The fx-85WA is a light calculator and pretty compact. The keys are pretty solid, but also allow for fast typing. I like the labeling of the keys, they are easy to read.

One thing I am big fan of both STO (store) and RCL (recall) are primary key functions. This is something we don’t see on scientific calculators anymore, as often either STO or RCL is a shifted function.

The color of the font on the keys and labels are readable with good contrast. The fx-85WA is a pleasure to use.

Verdict

The fx-85WA serves a scientific calculator providing with lots of functions. My only wish I had for this model is that top line’s font is bigger, but that is addressed in later models.

This model (and equivalent fx-300W) is a challenge to find. I searched ten pawn shops and several thrift shops for this model without success.

Before I go: I want to thank John Cadick for lending me his calculator to review.

I also want to give a table comparison of three Casio calculators:

(left to right) Casio fx-85WA, Casio fx-300MS, Casio fx-300ES Plus

	Casio fx-85WA	Casio fx-300MS	Casio fx-300ES Plus
Years (approximate)	About 1998-1999	About 2000 Manual Date: 3/2011, 3/2013	About 2004 Manual Date: 11/2011
Number of Keys	50, 2 are the left and right arrow keys	46 with keypad	46 with keypad
Number of Digits	10	10	10
Contrast the Screen?	No	Yes (newer versions)	Yes
Modes	[MODE]: COMP (Compute) SD (1-Var Stats) REG (2-Var Stats) Deg/Rad/Grad Fix/Sci/Norm	[MODE]: Comp (Compute) SD (1-Var Stats) REG (2-Var Stats) Deg/Rad/Grad Fix/Sci/Norm Disp (ab/c, d/c, Dot, Comma) Contrast (newer versions)	[MODE]: Comp (Compute) Stat (Statistics) Table (f(x), g(x)) [SETUP]: MathIO/LinearIO Deg/Rad/Grad Fix/Sci/Norm ab/c vs. d/c STAT (frequencies on) TABLE (f or f an g) Recurring Decimal Display (comma/decimal point) Contrast
Statistics Regressions	Linear, Logarithmic, Exponential, Power, Inverse, Quadratic	Linear, Logarithmic, Exponential, Power, Inverse, Quadratic	Linear, Quadratic, Logarithmic, Exponential, Power (both a*b^x and a*x^b), Inverse
Display	2-line display, top: entry, bottom: result	2-line display, top: entry, bottom: result	Textbook (can be set to 2-line display)
Exact Answers	Fractions	Fractions	Fractions, Square Root, Pi
Statistical Registers	Keyboard and Registers: A: ∑x^2, B: ∑x C: n, D: ∑y^2 E: ∑y, F: ∑xy, M: ∑x^3, X: ∑x^2y Y: ∑x^4	In two menus: S-SUM, S-VAR	In a menu: STAT
Statistical Data Entry	With the [M+] button, use semicolon (;) to input frequency	With the [M+] button, use semicolon (;) to input frequency	In a table, frequency column can be turned on or off in the SETUP menu
Multi-statement operations	No	Yes (with [ : ] )	Yes (with [ : ] )
Rect to Polar Conversions	E = r, F = θ	E = r, F = θ	X = r, Y = θ Answer is displayed
Polar to Rect Conversions	E = x, F = y	E = x, F = y	X = x, Y = y Answer is displayed
Extras	N/A	N/A	GCD, LMC, Int, Intg, RandInt, Factoring Integers (FACTOR)
Power	Solar/Batter Backup: LR44	Solar/Battery Backup: LR44	Solar/Battery Backup: LR44

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have questions.

Comparison – Three Generations of Casio fx-115

Casio fx-115D

Casio fx-115MS

Casio fx-115ES Plus

	Casio fx-115D	Casio fx-115MS	Casio fx-115ES Plus
Years (approximate)	1995	2000s	About 2008
Number of Keys	44	50 with keypad	50 with keypad
Number of Digits	10	10	10
Contrast the Screen?	No	Yes	Yes
Modes	[MODE]: Engineering Complex Numbers SD (1-Var Stats) LR (Linear Regression) DEG/RAD/GRAD FIX/SCI/NORM	[MODE]: Comp (Compute) SD (1-Var Stats) REG (2-Var Stats) Deg/Rad/Grad Fix/Sci/Norm Disp (ab/c, d/c, Dot, Comma) Contrast EQN: 2 x 2 linear system, 3 x 3 linear system, quadratic polynomial, cubic polynomial	[MODE]: Comp (Compute) Complex (complex numbers) Stat (Statistics) Base Table (f(x), g(x)) Equation: 2 x 2 linear system , 3 x 3 linear system, quadratic polynomial, cubic polynomial Vector Verify (comparison tests) [SETUP]: MathIO/LinearIO Deg/Rad/Grad Fix/Sci/Norm ab/c vs. d/c STAT (frequencies on) TABLE (f or f an g) Recurring Decimal Display (comma/decimal point) Contrast
Statistics Regressions	Linear	Linear, Logarithmic, Exponential, Power, Inverse, Quadratic	Linear, Quadratic, Logarithmic, Exponential, Power (both a*b^x and a*x^b), Inverse
Display	One line: classic post-fix notation	2-line display, top: entry, bottom: result	Textbook (can be set to 2-line display)
Exact Answers	Fractions (when they are used)	Fractions	Fractions, Square Root, Pi
Statistical Registers	On the keyboard	In two menus: S-SUM, S-VAR	In a menu: STAT
Statistical Data Entry	With the [M+] button	With the [M+] button	In a table
Multi-statement operations	N/A	Yes (with [ : ] )	Yes (with [ : ] )
Rect to Polar Conversions	View only (exchange answers with X ←→ Y)	E = r, F = θ	X = r, Y = θ Answer is displayed
Polar to Rect Conversions	View only (exchange answers with X ←→ Y)	E = x, F = y	X = x, Y = y Answer is displayed
Calculus Functions	None	Integral, Derivative, Solve for X	Integral, Derivative, Solve for X, Sum, Product
Variables	M, Kin/Kout 1-6	A,B,C,D,E,F,X,Y,M	A,B,C,D,E,F,X,Y,M
Extras	Engineering Symbols	Engineering Symbols	GCD, LMC, Int, Intg, RandInt, Factoring Integers (FACTOR)
Power	Solar/Battery Backup: G927	Solar/Battery Backup: LR44	Solar/Battery Backup: LR44

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

HP Prime, TI-84 Plus, and Casio fx-CG 50: Julian Date/Gregorian Calendar Conversions

HP Prime, TI-84 Plus, and Casio fx-CG 50:  Julian Date/Gregorian Calendar Conversions

Introduction

One conversion that is common in astronomy is to convert dates from our Gregorian calendar (the most commonly used day-to-day calendar) to a Julian Date Number, and visa versa.

JD:  Convert Gregorian Date to Julian Date Number

GREG:  Convert Julian Date Number to Gregorian Date

The Julian date number of 2451545 corresponds to January 1, 2000.

Gregorian Date to Julian Date Number

HP Prime Program JD:  Gregorian Date to Julian Date Number
Arguments:  four digit year, month, day
JD(y,m,d)

EXPORT JD(y,m,d)
BEGIN
// Gregorian to Julian
// year, month, day
// 2019-01-12 EWS
//  Wikipedia
LOCAL x0:=IP((m-14)/12);
LOCAL x1:=IP(((1461*(y+4800+x0))/4));
LOCAL x3:=IP(367*(m-2-12*x0)/12);
LOCAL x5:=IP((y+4900+x0)/100);
LOCAL x6:=IP(3*x5/4);
LOCAL j:=x1+x3-x6+d-32075;
RETURN j;
END;

TI-84 Plus Program JD:  Gregorian Date to Julian Date Number

"GREGORIAN TO JULIAN"
"2019-01-13 EWS"
Input "YEAR: ",Y
Input "MONTH: ",M
Input "DAY: ",D
iPart((M-14)/12)→X
iPart(((1461*(Y+4800+X))/4))→A
iPart(367*(M-2-12*X)/12)→B
iPart((Y+4900+X)/100)→C
iPart(3*C/4)→C
A+B-C+D-32075→J
Disp "JD: ",J

Casio fx-CG50 Program JD:  Gregorian Date to Julian Date Number
This version can be typed in directly in the calculator (not a text file)

"GREGORIAN TO JULIAN"
"2019-01-19 EWS"
"YEAR?"→Y
"MONTH"?→M
"DAY"?→D
Int ((M-14)÷12)→X
Int (((1461×(Y+4800+X))÷4)) →A
Int (367×(M-2-12×X)÷12) →B
Int ((Y+4900+X) ÷ 100) →C
Int (3×C÷4)→C
A+B-C+D-32075→J
ClrText
Locate 1,1,"JD"
Locate 1,2,J

Julian Date Number to Gregorian Date

HP Prime Program GREG:  Julian Date Number to Gregorian Date
Argument:  Julian Date Number
GREG(j)

EXPORT GREG(j)
BEGIN
// Julian to Gregorian
// Wikipedia
// 2019-01-12 EWS
LOCAL x1:=IP((4*j+274277)/146097);
LOCAL x2:=IP(x1*3/4);
LOCAL f:=j+1401+x2-38;
LOCAL E:=4*f+3;
LOCAL G:=IP((E MOD 1461)/4);
LOCAL H:=5*G+2;
LOCAL D:=IP((H MOD 153)/5)+1;
LOCAL M:=((IP(H/153)+2) MOD 12)+1;
LOCAL Y:=IP(E/1461)-4716+IP((12+2-M)/12);
RETURN {Y,M,D};
END;

TI-84 Plus Program GREG:  Julian Date Number to Gregorian Date

"JULIAN TO GREGORIAN"
"2019-01-13 EWS"
Input "JD: ",J
iPart((4*J+274277)/146097)→X
iPart(X*3/4)→X
4*(J+1401+X-38)+3→E
5*iPart(remainder(E,1461)/4)+2→H
iPart(remainder(H,153)/5)+1→D
remainder(iPart(H/153)+2,12)+1→M
iPart(E/1461)-4716+iPart((12+2-M)/12)→Y
Disp "YEAR, MONTH, DAY:",Y,M,D

Casio fx-CG50 Program GREG: Julian Date Number to Gregorian Date 
This version can be typed in directly in the calculator (not a text file)

"JULIAN TO GREGORIAN"
"2019-01-13 EWS"
"JD"?→J
Int ((4 ×J+274277) ÷146097) →X
Int (X ×3 ÷4) →X
4 ×(J+1401+X-38)+3 → E
5 × Int( MOD(E,1461) ÷ 4)+2 → H
MOD(Int  (H ÷153)+2,12)+1 →M
Int (E ÷1461) -4716+Int ((12+2-M) ÷12) → Y
ClrText
Locate 1,1,"YEAR, MONTH, DAY"
Locate 1,2,Y
Locate 1,3,M
Locate 1,4,D

Examples

Gregorian Date:  1988, October 31
JD:  2447466

Gregorian Date:  1999, January 11
JD:  2451190

Gregorian Date:  2017, March 21
JD:  2457834


Source:

"Julian Day"  Wikipedia.  Edited (when retrieved) November 19, 2018.  Retrieved January 11, 2019.  https://en.wikipedia.org/wiki/Julian_day

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

TI-84 Plus CE: Lower Case Letters without Assembly

TI-84 Plus CE:  Lower Case Letters without Assembly

Letter Case Letters without Assembly Programs

It is possible to put letter case letters in TI-84 Plus CE programs without running an assembly program.  This is going to require the use of the TI Connect CE computer program.  I am using the Windows version and hopefully my assumption will be correct that this technique will work on the Mac version as well.

Note: You will need the TI-84 Plus CE (the newest, thinnest TI-84) for this.  The TI-84 Plus CE has a back-lit, color screen. 

Steps:

1.  Connect your TI-84 Plus CE to your computer.

2.  Start up the TI Connect CE computer program.

3.  Select PROGRAM EDITOR on the left hand menu.  Next, click on New Program (the folder with the plus key) on the right.  (You can also edit programs but we'll create a new program for this demo.)

4.  Name your program.  For this example, I am going to name it DEMO.  The name can be in lower case, but the letters in the name will become upper case when the program is transferred to the TI-84 Plus CE. 

5.  Type your program.  You can use the catalog on the left to insert commands.  The Keypad section is where you insert pi (π), the store arrow (→), the square root function (√), the exponential function (e^), and the imaginary indicator to build complex numbers (i = √-1). 

We will need to type the program in the Program Editor software, not directly on the TI-84 Plus CE calculator. 

This is my demo program.

TI-84 PLUS CE Program DEMO

Disp "This is a test program."
Input "a: ",A
Input "b: ",B
A^2+B^2→C
A^3+B^3→D
ClrHome
Disp "Results:","a^2+b^2=",C
Disp "a^3+b^3=",D

Notes:

*  Variables must still be in uppercase. 

*  You can use lower case letters with programming through the software, but Unicode characters do not transfer over. 

6.  Save your program (if you want). 

7.  If you have not already, turn on the TI-84 Plus CE.  Then send the program to your TI-84 Plus CE.  There are three ways to accomplish this task (Windows):

* Click on the Send Program to Connect Calculator icon.
* Key Ctrl+E.
* Under the Actions menu, click on the Send to Calculators menu.

If the program is accepted, you program is transferred.

8.  Run the program on your calculator.

Limitations

*  Using lower case in this method requires editing on the program software, not the calculator itself.

*  You must still use single upper case letters for variables.

*  I have not been able to do Unicode characters with this method, as the calculator program will not transfer.

*  This lower case is useful for displaying messages and prompts. 

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

HP 42S Polynomial Operations

HP 42S Polynomial Operations

Note: These programs presented in today's blog are can also be programmed on the Free42 app and the DM 42.  The default setting, 25 memory registers, is assumed to be set.  The programs are written use R24 as a counter. 

This program uses indirect storage (R24).  The maximum order is 23.

HP 42S Program SPOLY

This program asks for the order of a polynomial and then asks the user to store the coefficients.  The order of registers are coefficients of powers of x in descending order from n to 0. 

For example, for a cubic polynomial, the coefficients are stored as such:
R01 = coefficient of x^3
R02 = coefficient of x^2
R03 = coefficient of x
R04 = constant coefficient

Program:

00 { 67-Byte Prgm }
01▸LBL "SPOLY"
02 CLX
03 "ORDER?"
04 PROMPT
05 STO 00
06 IP
07 1
08 +
09 1ᴇ-3
10 ×
11 1
12 +
13 STO 24
14▸LBL 00
15 "X↑"
16 RCL 00
17 RCL 24
18 IP
19 -
20 1
21 +
22 ARCL ST X
23 ├" ="
24 CLX
25 PROMPT
26 STO IND 24
27 ISG 24
28 GTO 00
29 "DONE"
30 AVIEW
31 RTN
32 END

Example:  Store the polynomial p(x) = 2*x^3 - x^2 + 5*x + 7

Keystrokes:  [ XEQ ] (SPOLY)
"ORDER?" 3 [ R/S ]
"X↑3.0000=" 2 [R/S]
"X↑2.0000=" 1 [ +/- ] [R/S]
"X↑1.0000=" 5 [R/S]
"X↑0.0000=" 7  [R/S]
"DONE"

Results
R01 = 2.0000
R02 = -1.0000
R03 = 5.0000
R04 = 7.0000

HP 42S Program HORNER

The HORNER evaluates the polynomial p(x).  The assumes that the order of registers are coefficients of powers of x in descending order from n to 0.  The user is asked about the order of the polynomial and the value of x.

Program:

00 { 65-Byte Prgm }
01▸LBL "HORNER"
02 CLX
03 "X?"
04 PROMPT
05 STO 00
06 CLX
07 "ORDER?"
08 PROMPT
09 IP
10 1ᴇ-3
11 ×
12 1
13 +
14 STO 24
15 RCL 00
16 RCL× IND 24
17 ISG 24
18▸LBL 01
19 RCL+ IND 24
20 RCL× 00
21 ISG 24
22 GTO 01
23 RCL+ IND 24
24 "P(X)="
25 AVIEW
26 RTN
27 .END.

Example:  Let p(x) be the polynomial, p(x) = 2*x^3 - x^2 + 5*x + 7
Calculate p(-3).

The coefficients are have already been stored (from last example).
R01 = 2.0000
R02 = -1.0000
R03 = 5.0000
R04 = 7.0000

Keystrokes:  [XEQ] (HORN)
"X?" 3 [ +/- ] [ R/S ]
"ORDER?" 3  [ R/S ]

Result:  -71.0000

HP 42S Program DX_PX

This program calculates coefficients of the derivative of the polynomial p(x), using the form:

d/dx x^n = n * x^(n-1)

The order of registers are coefficients of powers of x in descending order from n to 0. 

Program:

00 { 79-Byte Prgm }
01▸LBL "DX_PX"
02 CLX
03 "ORDER?"
04 PROMPT
05 STO 00
06 IP
07 1ᴇ-3
08 ×
09 1
10 +
11 STO 24
12▸LBL 02
13 RCL IND 24
14 RCL 00
15 RCL 24
16 IP
17 -
18 1
19 +
20 ×
21 STO IND 24
22 "X↑"
23 RCL 00
24 RCL 24
25 IP
26 -
27 ARCL ST X
28 X<>Y
29 AVIEW
30 STOP
31 ISG 24
32 GTO 02
33 1
34 RCL+ 00
35 STO 24
36 CLX
37 STO IND 24
38 "DONE"
39 AVIEW
40 RTN
41 .END.

Example:  Calculate the derivative of p(x) = 2*x^3 - x^2 + 5*x + 7.  Assume that coefficients from the previous example.

Keystrokes:  [ XEQ ] (DX_PX)
"ORDER?" 3 [R/S]

Results:
"X↑2.0000=" 6.0000 [R/S]
"X↑1.0000=" -2.0000 [R/S]
"X↑0.0000=" 5.0000  [R/S]
"DONE"

dp/dx = 6*x^2 - 2*x + 5

Registers:
R1 = 6.0000
R2 = -2.0000
R3 = 5.0000
R4 = 0.0000

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

Review: Casio DJ-120D

Review:  Casio DJ-120D

Type:  Desktop
Number of Digits: 12
Power:  Solar with Battery Backup (LR44)
Operating Mode: Chain

Large Size Calculator

This calculator is huge.  The keyboard is nice and large.  The keys are large, that you can easily rapidly type calculations.  The screen is also large, making the numbers the screen easy to read. 

The keyboard has a double zero ( [00] ) and a a triple zero ( [000] ) key, you can enter large numbers rapidly. 

Display Options

There are many display options, primarily by two switches.  One switch sets the number of decimal points (0 through 4 and add mode).  The other switch determines how numbers are rounded (float (not at all), cut (truncated), up (round up), and 5/4 (regular rounding)). 

You can set additional displays modes, such as comma or decimal point for fractional marks using the [ AC ]/[DISP] key and scrolling through the options.  You actually make two settings.  Those two settings get toggled with the [DISP] key in regular calculator mode. 

Add Mode

Add mode allows numbers to be added and subtracted in "dollars and cents" (divided by 100).  The automatic division by 100 is not affected by multiplication and division.  Add Mode is activated when the rounding mode is set to either cut, up, or 5/4. 

Reviewing and Editing Calculations

The DJ-120D has a 150 step memory.  All the arithmetic calculations are stored in each step.  Historical calculations are finalized by either pressing the equals sign [ = ] or the percent sign [ % ].  Calculations can be reviewed by using the arrow keys, the [GO TO] key, or the [AUTO REVIEW] key. 

When you are using the review feature, the display may not be intuitive.  For the arithmetic and percent sign, the function is read on the top of screen.  When you conclude a calculation, the display will show the equals sign on the left side of the screen.  This takes getting used to. 

Example:  Reviewing the Calculations

1120 [+ ]
365 [ - ]
630 [ = ]  

The result is 855.

Review of the calculations:

01  REV  1120 +
02  REV  365 -
03  REV  =  630
04  REV  ANS 855

Note how the equals sign is on the left, not on the right.  It may be confusing to read at first.  Also, square root operations affects only the number in history, the square root function is not recorded as a step. 

While editing operations, you can correct steps.  For example, I change the first step to 1210 +. 

[GO TO] 1 [GO TO]
[CORRECT] 1210 [ + ] [CORRECT]

Reviewing the steps:

01  REV  1210 +
02  REV  365 -
03  REV  =  630
04  REV  ANS 945

The Grand Total Feature

The DJ-120D has a Grand Total feature.  This accumulates every calculation that is completed by pressing the equals key.  You can recall the grand total by pressing [ GT ].   The grand total is a separate memory register.

Example:

46 [ + ] 43 [ = ]  (89)
100 [ - ] 57 [ = ]  (43)
5 [ * ] 9 [ = ]  (45)
[GT] returns 177.  (89 + 43+ 45)

The all clear key [AC] (also ON) clears both the grand total and history.

The Markup Key

The markup key [MU] performs the operation x/(1 - p%). 

Verdict

I love the large keyboard and the display.  I would recommend this calculator for students who are learning math (the review function makes it useful to review math calculations), and office professionals.

Eddie


All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

Solar Scientific Calculators: Dealing with Integrals with Infinite Limits

Solar Scientific Calculators:  Dealing with Integrals with Infinite Limits

Integrals with Infinite Limits

Today's post deals with integrals with infinite limits in the forms:

∫( f(x) dx, x = a to x = ∞)

∫( f(x) dx, x = -∞ to x = ∞)

∫( f(x) dx, x = -∞ to x = a)

One method to deal with these integrals, as suggested by W.A.C. Mier-Jedrzejowicz Ph. D. (see the source), is to use the substitution

x = tan θ

Then:

dx = dθ/cos^2 θ

and θ = atan x.

Also, as x approaches π/2, tan x approaches +∞.

And, as x approaches -π/2, tan x approaches -∞.

With the substations, let's test four integrals on four solar-powered scientific calculators:

1.  Casio fx-991EX Classwiz
2.  Sharp EL-W516T
3.  Texas Instruments TI-36X Pro
4.  Casio fx-115ES Plus

Set the calculator to radians mode. 

Example 1:  ∫(1/x^2 dx, x = 1 to x = ∞) = 1

∫(1/x^2 dx, x = 1 to x = ∞)

with the substitutions x = tan θ and dx = dθ/(cos^2 θ):

∫( 1/tan^2 θ * dθ/cos^2 θ, θ = atan 1 to θ = π/2)

∫( 1/sin^2 θ * dθ, θ = atan 1 to θ = π/2)

We can evaulate the integral straight away.  Here are the results:

1.  Casio fx-991EX Classwiz
Time: 1.37 seconds
Answer: 1

2.  Sharp EL-W516T
Time: 38 seconds
Answer: 1

3.  Texas Instruments TI-36X Pro
Time: 4.5 seconds
Answer: 1

4.  Casio fx-115ES Plus
Time: 4.2 seconds
Answer: 1

A promising start.

Example 2:  ∫(e^(-0.5*x^2), x = 0 to x = ∞) ≈ 1.25331413732

∫(e^(-0.5*x^2), x = 0 to x = ∞)

with the substituions, this becomes:

∫(e^(-0.5 * tan^2 θ)/cos^2 θ dθ, θ = atan 0 to θ = π/2)

atan 0 = 0

But look at the denominator, we have cos^2 θ.  Since cos^2 π/2 = 0, there will be a problem.  Let's use an approximation of π/2 of 1.5708.

∫(e^(-0.5 * tan^2 θ)/cos^2 θ dθ, θ = 0 to θ = 1.5708)

Here are the results:

1.  Casio fx-991EX Classwiz
Time: 15.4 seconds
Answer: 1.253314137

2.  Sharp EL-W516T
Time: 1 minute, 8 seconds
Answer: errors out

3.  Texas Instruments TI-36X Pro
Time: 36 seconds
Answer: 1.253314138

4.  Casio fx-115ES Plus
Time: 1 minute, 6.8 seconds
Answer: 1.253314137

Example 3:  ∫(x^2*e^-x dx, x = 0 to x = ∞) = 2

∫(x^2*e^-x dx, x = 0 to x = ∞)

with the substitutions and simplification, we get:

∫( (sin^2 θ * e^(-tan θ))/cos^4 θ dθ, θ = 0 to θ = π/2)

Like the last situation, there is a potential problem with the denominator.  Let's see if we can use an approximation of π/2, this time using 1.57 in hopes to cut the calculation time down.

∫( (sin^2 θ * e^(-tan θ))/cos^4 θ dθ, θ = 0 to θ = 1.57)

Here are the results:

1.  Casio fx-991EX Classwiz
Time: 27 seconds
Answer: 2

2.  Sharp EL-W516T
Time: 1 minute, 34 seconds
Answer: 1.999999999

3.  Texas Instruments TI-36X Pro
Time: 1 minute, 9 seconds
Answer: 2

4.  Casio fx-115ES Plus
Time: 1 minute, 6.8 seconds
Answer: 1.253314137

Example 4:  ∫( e^-x/x^2 dx, x = 1 to x = ∞) ≈ 0.148495506776

∫( e^-x/x^2 dx, x = 1 to x = ∞)

with the substitutions and simplification, we get:

∫( e^(-tan θ)/sin^2 θ dθ, θ = 0 to θ = π/2)

I'm going to use the 1.57 approximation again and set the integral as:

∫( e^(-tan θ)/sin^2 θ dθ, θ = 0 to θ = 1.57)

Here are the results:

1.  Casio fx-991EX Classwiz
Time: errors out immediately
Answer: N/A

2.  Sharp EL-W516T
Time: 1 minute, 6 seconds
Answer: error

3.  Texas Instruments TI-36X Pro
Time: 7 seconds
Answer: 0.148495519

4.  Casio fx-115ES Plus
Time: errors out after 1 second
Answer: N/A

Some Observations

1.  Not all calculations of improper integrals will be successful.

2.  Out of the four calculators tested, from the four calculations:  the Casio fx-991ES is the fastest, but I found the most successful with the Texas Instruments TI-36X Pro.

3.  Be ready to spend a little for calculations by using this method.

Source:

Mier-Jedrzejowic, W.A.C. Ph.D.  Extend Your 41  London, UK 1985  ISBN 0-9510733-0-03

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

HP Prime and HP 42S: Noise Figure and Noise Voltage

HP Prime and HP 42S:  Noise Figure and Noise Voltage

Notes:  The programs for the HP 42S format are designed to work with the HP 42S's solver.  The programs were created using Thomas Okken's Free42, and should also be compatible with the Swiss Micros DM42.

Noise Figure

Given system temperature (in Kelvins), this program calculates the noise figure (in Decibels), which describes the noise performance of an amplifier.  The noise figure is described as the difference between the noise output of an actual receiver to an ideal, noiseless receiver.  A noiseless receiver is said to have a resistor operating at room temperature, 290 K (about 16.85°C or 62.33°F). The lower the noise figure, the better.

Formula:

F = 10 * log(T/290 + 1)

where:

F = noise figure (dB)
T = system temperature (K)

HP Prime Program Function:  NOISEDB

EXPORT NOISEDB(T)
BEGIN
// Noise Figure in dB
// Input: T: Temperature (K)
// 2019-01-04 EWS
10*LOG(T/290+1);
END;

HP 42S Program for Solver:  NSEFG

00 { 35-Byte Prgm }
01▸LBL "NSEFG"
02 MVAR "F"
03 MVAR "T"
04 RCL "T"
05 290
06 ÷
07 1
08 +
09 LOG
10 10
11 ×
12 RCL "F"
13 -
14 END

Example (Fix 4):

Input:  T = 57.8°F, convert it to Kelvins, enter 287.4833 K (approximately)
Result:  F = 2.9914 dB

Noise Voltage

Given the noise bandwidth (in Hertz) and the resistance (in Ω), calculate the open-circuit voltage (in RMS volts).

Formula:

e_n = √(1.6*10^-20 * B * R)

where:

e_n = open circuit voltage noise (RMS volts)
B = bandwidth (Hz)
R = resistance (Ω)

HP Prime Program Function: NOISEVOLT

EXPORT NOISEVOLT(b,r)
BEGIN
// Noise Voltage in V
// Input: B=bandwidth (Hz)
// Input: R=resistor (Ω)
// input numbers only
√(1.6ᴇ−20*b*r);
END;

HP 42S Program for Solver:  NSEVT

00 { 37-Byte Prgm }
01▸LBL "NSEVT"
02 MVAR "B"
03 MVAR "R"
04 MVAR "En"
05 16ᴇ-21
06 RCL× "B"
07 RCL× "R"
08 SQRT
09 RCL- "En"
10 .END.

Example (FIX 4):

Input:  B = 31,000 Hz, R = 950 Ω
Result:  e_n = 6.8644e-7 V

Sources: 

Ball, John A.  Algorithms For RPN Calculators  John Wiley & Sons: New York  1978.  ISBN 0-471-03070-8

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

HP Prime and Casio fx-5800p: Rational Binomial Coefficients

HP Prime and Casio fx-5800p:  Rational Binomial Coefficients

Introduction

Let p be a rational fraction, p = num/dem.  The rational binomial coefficients of order n are defined by:

B_0(p) = 1

B_n(p) = COMB(p, n) = ( p * (p - 1) * (p - 2) * (p - 3) * ... * (p - n + 1) ) / n!

There are algorithms, but the program RATBIN uses the definition. 

HP Prime Program RATBIN

Arguments:  rational fraction, order

EXPORT RATBIN(p,n)
BEGIN
// 2018-12-26 EWS
// p-q, n
// Rational Binomial Coefficient
LOCAL X;
IF n==0 THEN
RETURN 1;
ELSE
IF n==1 THEN
RETURN p;
ELSE
RETURN QPI(ΠLIST(p-MAKELIST(X,X,0,n-1))/n!);
END;
END;
END;

* Note: the result is not always a fraction, but you can convert the answer to fraction by pressing [ a b/c ]

Casio fx-5800p Program RATBIN

For fractional results, use the fraction button [  []/[] ].

"2018-12-26 EWS"
"FRACTION"? → P
"ORDER?" → N
If N=0
Then
0
IfEnd
If N=1
Then
1
IfEnd
If N>1
Then
Prod (P-Seq(X,X,0,N-1,1)) ÷ N! → Q
Q
IfEnd

Examples

b_2(1/2) = -1/8

b_3(1/2) = 1/16

b_4(1/2) = -5/128

b_5(1/2) = 7/256

Source:

Henrici, Peter.  Computational Analysis With the HP-25 Calculator  A Wiley-Interscience Publication. John Wiley & Sons: New York 1977 .  ISBN 0-471-02938-6

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

Celebrating the New Year With 2019: 19 Ways to Mathematically Express 2019

Celebrating the New Year With 2019

HAPPY NEW YEAR!!!

19 Ways to Mathematically Express 2019

2019 = 3 * 673  (Prime Factorization)

2019 = 2^10 + 2^9 + 2^8 + 2^7 + 2^6 + 2^5 + 2 + 1

2019 = 3 + 2 * (3^6 + 3^5 + 3^3 + 3^2)

2019 = 42^2 + 4^4 - 1

2019 = 41^2 + 7^3 - 5

2019 = 4^5 + 3^6 + 2^8 + 10

2019 = 11^3 + 5^4 + 2^6 - 1

2019 = 12^3 + 17^2 + 2

2019 = int(10^3.3) + int(e^3) + 2^2   (e = 2.718281828...,  int: integer function)

2019 = 2 * (10^3 + 9.5)

2019 = 3^7 - 13^2 + 1

2019 = 4 * 505 - 1

2019 = 2 * 6! + 4 * 5! + 16 * 3! + 3

2019 = (10^4 + 19 * 5) / (2^2 + 1)

2019 = (13^4 - 12^3 - 9^3 + 12^2 - 1) / (2^2 + 3^2)

2019 = (2^13 + 3^8 + 4^5 + 5^3 + 6^3 + 34) / 8

2019 = 50 * 19 + 50 * 18 + 9 * 17 + 16

2019 = 25 * 19 + 25 * 18 + 26 * 13 + 71 * 11

2019 = √(4 * 10^6 + 7 * 10^4 + 6 * 10^3 + 3 * 10^2 + 6 * 10 + 1)

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.