Friday, July 10, 2020

Retro Review: TI-95 Procalc

Retro Review:  TI-95 Procalc 





This review covers the calculator itself, not any of the optional accessories which includes a thermal printer and cassette interface. 


Quick Facts:

Model:  TI-95 Procalc
Company:  Texas Instruments
Type:  Scientific, Keystroke Programmable
Years:  1985-1987
Display:  10 digits for numerical answers, 16 alpha-numeric display
Batteries:  4 AAAs
Logic:  Algebraic (AOS)
Original Price:  $200.00.  I paid $60 I bought it on eBay.

Memory:
Registers:  26 alpha registers, up to 900 numeric registers (three digit registers)
Programming Steps: up to 7,200 steps, default set at 1,000 steps.
Storage Memory:  up to 8,000 bytes, set to 5,200 bytes by default.

A separate 8K RAM can be added for an additional 8,000 bytes of memory.

The QWERTY Keyboard and Other Unique Features

One look at the keyboard and one may mistake the TI-95 Procalc as a BASIC Programming calculator.  However, the TI-95 Procalc is a keystroke programmable calculator.   We'll talk about the programming later.

The TI-95 Procalc is one of the first calculators to contain function keys, F1 through F5.

In addition to the standard functions including trigonometry, logarithms, roots, powers, factorials, hyperbolic functions, and statistics including linear regression:

The number menu [ NUM ] has functions including integer part (INT), fractional part (FRC), random numbers between 0 and 1 (R#), round the number displayed to fix number settings (RND), sign function (SGN), lowest common multiple (LCM), prime factors (PF), and absolute value (ABS).

The LCM soft key has two functions:

(LCM) :   lowest common multiple. 
 Example:  4 [ x~t ] 6 (LCM) returns LCM = 12.

(LCM) [ x~t ]: greatest common divisor.
Example:  25 [ x~t ] 40 (LCM) [ x~t ] returns 5   (GCD(25, 40) = 5)

(PF) returns the biggest prime factor of an integer.  To get additional prime factors, repeat the keystrokes [ x~t ] (PF).

Example:  28
28 [ NUM ] [ --> ] ( PF ) returns  f = 2
[ x~t ] ( PF ) returns f = 2
[ x~t ] ( PF ) returns f = 1  (When you reach f = 1, press [ x~t ] to get the last prime factor, 7)
28 = 2 * 2 * 7 = 2^2 * 7

The conversions menu [CONV] contain several types of conversions:

MET (Metric):
(F - C)  °F -> °C  (left to right),  [INV] (F - C) does °C -> °F  (right to left)
All of the conversions follow this pattern.
(G - L)  gallon and litre
(# - K)  pounds (#) and kilograms (kg)
(i - m)  inches (i) and millimetres (m)
(f - M)  feet and meters

DMS:  convert to D.MMSSS from degrees
INV DMS:  convert degrees to D.MMSSSS

ANG:  convert between Degrees (D), Radians (R), and Grads (G)

P-R:
r [ x~t ] θ [ P-R ] results:  y [ x~t ] x  (polar to rectangular)
x [ x~t ] y [ INV ] [P-R] results: θ [ x~t ] r   (rectangular to polar)

BAS:  (Bases)
DEC: convert to base 10 and set the TI-95 Procalc to Decimal Mode
HEX:  convert to base 16 and set the TI-95 Procalc to Hexadecimal Mode
OCT:  convert to base 8 and set the TI-95 Procalc to Octal Mode
2sC:  convert to 2's complement format
UNF:  convert to un-formatted display mode

Two things to note:
1.  Hexadecimal numbers A-F are accessed with the [ 2nd ] key.
2.  There are no conversions to binary integers

The FUNC key has three operations:

QAD:  Find the roots, real or complex, of the quadratic equation a*x^2 + b*x + c = 0

CUB:  Find the roots of the cubic equation a*x^3 + b*x^2 + c*x + d = 0

SYS:  This is not a solver for system of equations.  Instead, it allows the user to turn system protection on or off.  With system protection off, the user can edit specific bytes of memory.  The aim for unprotected system memory mode is to assist the user in assembly programming.

Fun Fact:  FIX 9 sets the TI-95 Procalc to floating mode.

One more fun fact:  The factorial functions accepts arguments of both integers and integers in the form of n + 1/2.   The latter can include negative numbers.  You will not see this in any other standard scientific calculator (outside the CAS-enabled factorials).

Help: But Not What You Expect

The HELP key does not give help on the specific functions.   Instead, the HELP key asks the user "SET NORMAL MODE?".  Yes resets the TI-95 to decimal mode, floating standard mode (removes Fix settings), degree mode, and sets memory partition to default (1000 program steps, 125 numeric registers, and 5200 bytes for files).  A No asks the user whether to reset any specific mode that is set to default.

Files, Files, and More Files

The FILES key is where you would store, load, and delete program and data files.  Files have three characters (fixed so the file "A   " has A followed by two spaces).  FILES is also where you access the 8K RAM or additional RAM cartridges.   It's pretty neat how the FILES system works once it is learned.

The ALPHA Register

Similar to the HP 41C and HP 42S, the TI-95 Procalc has a 16 character ALPHA register.  The ALPHA register is used to display results and prompt messages.  Numeric registers call be recalled into the ALPHA register.

Example:  11 is stored in register A.  ANSWER = is in the ALPHA register.  Pressing (COL) 16, moves the cursor to column 16.   (MRG) A places 11 at the 16th space justified right.

ALPHA register:   ANSWER =     11.

MRG = recalls the number from the display/last answer.

The ALPHA register can contain lower case letters and ASCII characters simular to the TI-58/59 family.

Keystroke Programming

The TI-95 Procalc has algebraic keystroke programming with labels, tests against numeric registers, increase and decrease by 1 (INCR and INV INCR, respectively) functions, define menus (DEF), the use of ALPHA register.

Unique is the YES/NO function.  Y/N creates a two function menu (F1: YES, F2: NO) and works like the rest of the test commands.

Y/N
(do if YES is pressed)
(skip to here if NO is pressed)

Labels are two characters which can contain both numbers and letters.  Go to and subroutines to labels are use the commands GTL and SBL.

The halt command, HLT, stops program execution.  While the break command, BRK temporarily stops the program execution to display the current result and sets F1 to GO.

Storage arithmetic is permitted.

Example program:  PRF which automates the prime factors of an integer.

TI-95 Procalc Program: Prime Factors


STO A
'NUMBER?' 
BRK
LBL 00
PF 
'FACTOR = '
COL 16 
MRG =
BRK
IF= A
GTL 01
x~t
GTL 00
LBL 01
x~t
'FINAL = '
COL 16
MRG =
HLT  

(50 steps)

Example: 158
'NUMBER?' 158 (GO)
'FACTOR=        2.'  (GO)
'FACTOR=        1.'  (GO)
'FINAL=        79.'

158 = 2 * 79

The TI-95 Procalc comes with a har dcase and a gray help card.

Verdict

I like this calculator, having a solid set of functions with adjustable programming space.   Having the 8K RAM card, which came with the calculator when I bought it, allows me store programs on the card without having to worry about storage space as much.

There are several things I have to get used to: the program steps scroll horizontally instead of vertically, and both the break (BRK) and halt (HLT) operate differently from the modern definition.  Thankfully both the operating and programming manuals are still available online through the Datamath website.

The price point is pretty high at $200.00, as the TI-95 Procalc was set as Texas Instruments' high end programmable keystroke programmable.

The Datamath page has an emulator:  http://www.datamath.org/Graphing/TI-95.htm

Eddie

Source:

Woerner, Joerg.  "Texas Instruments TI-95 PROCALC"  Datamath  http://www.datamath.org/Graphing/TI-95.htm  Last Edited December 5, 2001.  Accessed June 22, 2020.

All original content copyright, © 2011-2020.  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.

Sunday, July 5, 2020

Casio fx-991EX and fx-115ES Plus: Velocity Conversions

Casio fx-991EX and fx-115ES Plus: Velocity Conversions

The Casio fx-991EX Classwiz and Casio fx-115ES Plus calculators, among others, have 40 conversions in various areas. 

Keystrokes

Keystrokes: Casio fx-115ES Plus

[ SHIFT ] [ 8 ], enter the required two digit code

The conversions we'll be working with this blog entry:

ft → m, 03
m → ft, 04
yd → m, 05
m → yd, 06
mile → km, 07
km → mile, 08
km/hr → m/s, 19
m/s → km/hr, 20

Keystrokes:  Casio fx-991EX Classwiz

[ SHIFT ] [ 8 ].    The conversions will be grouped by category (length, area, volume, etc).

ft → m, 1, 3
m → ft, 1, 4
yd → m, 1,5
m → yd, 1,6
mile → km, 1, 7
km → mile, 1, 8
km/hr → m/s, ↓, 1, 1
m/s → km/hr, ↓, 1, 2

km/hr  (kilometers per hour) vs mph (miles per hour)

The calculators mentioned does not have a direct conversion between km/hr and mph.  However, because the time frame is the same (per hour), we can use the km/mile conversions (since 1 hour = 1 hour and no time conversion part is required, only the length).

Example 1:  150 km/hr to mph

150 km>mile returns 93.20567884

150 km/hr = 9320567884 mph

Example 2:  65 mph to km/hr

65 mile>km = 104.60736

65 mph = 104.60736 km/hr

More Examples

Example 3:  5.8 ft/s to m/s

Again, since the time portion is the same (second to second), we only have to worry about length.

5.8 ft>m returns 1.76784

5.8 ft/s = 1.76784 m/s

Example 4:  110 ft/s to km/hr

Now we are converting both length and time.   There are no direct time conversions on the calculators featured, so we have to use the manual conversion. 

Remember that 1 hr = 3600 s and 1 km = 1000 m. To convert from m to km, divide by 1000 and to convert from 1/s to 1/hr, multiply by 3600 (note: 1/s to 1/hr)

(110 ft>m) ÷ 1000 × 3600 returns 120.7008

110 ft/s = 120.7008 km/hr

Example 5:  40 m/s to km/hr

Here is another example where we both have to convert the length (m to km) and time component (1/s to 1/hr).   This is similar to the Example 3.  However, the Casio calculators featured on this blog has conversions between m/s and km/hr (velocity section).

40 m/s>kh/hr returns 144 km/hr

40 m/s = 144 km/hr

Example 6:  100 ft^2 to m^2

The calculators have two area conversions (acre/m^2).   However, we can use the same length conversion twice to make other areas.

100 ft>m ft>m returns 9.290304

100 ft^2 = 9.290304 m^2

Example 7:  1 mi to yd by using the conversions available

(1 mi>km × 1000) m>yd returned 1760

(1 km = 1000 m)

1 mi = 1760 yd

A Cautionary Tale

Example 8:  1 acre to ft^2

1 acre>m^2 m>ft m>ft returns 43559.99545

However, as defined, 1 acre = 43560 ft^2. 

Lesson:  use caution when chaining conversions, 100% accuracy isn't guaranteed.

Eddie

All original content copyright, © 2011-2020.  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

Friday, July 3, 2020

Casio fx-9750GIII: Sequence of Rotated Points

Casio fx-9750GIII: Sequence of Rotated Points

Introduction

The program ROTSEQ generates a 2 row matrix from the sequence:

[ [ x_n+1 ] [ y_n+1 ] ] = A * [ [ cos θ, -sin θ ] [ sin θ, cos θ ] ] * [ [ x_n ] [ y_n ] ]

The required inputs are:
You will set the angle mode to Degree, Radian, or Gradian
A = multiplier
θ = angle
x1 = initial x point
y1 = initial y point
N = number of steps

Casio fx-9750GIII Program ROTSEQ

This can be used on most if not every modern Casio Graphing calculator.

"EWS 2020-06-07"
Menu "ANGLE","DEGREE",1,"RADIAN",2,"GRADIAN",3
Lbl 1:Deg:Goto 4
Lbl 2:Rad:Goto 4
Lbl 3:Gra:Goto 4
Lbl 4
"F=A*MAT*[[X][Y]]"
"A"?->A
"θ"?->θ
"X1"?->X
"Y1"?->Y
"STEPS"?->N
[[X][Y]]->Mat A
Mat A->Mat B
For 1->I To N
[[cos θ,-sin θ][sin θ,cos θ]]*Mat A->Mat A
Augment(Mat B,Mat A)->Mat B
Next
"FINAL RESULTS:"◢
Mat B

Example

A = 0.5
θ = 10 grads  (Gradian mode)
x1 = 1
y1 = -1
N = 5  (5 steps)

I don't think I ever used gradian angle units on this blog before, so why not?

Results are shown and rounded to 2 decimal places

Mat B:

[ 1.00   1.14   1.26   1.34   1.40   1.41 ]
[ -1.00  -0.83  -0.64 -0.44  -0.22  0.00 ]

The next blog post will be on July 5 since tomorrow will be the 4th of July (Happy Birthday, United States). 

Eddie

All original content copyright, © 2011-2020.  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.

Sunday, June 28, 2020

Numworks Python Scripts: Basic Graphics

Numworks Python Scripts:  Basic Graphics

Script:  atari.py

Draws the basic-eight color palette of the classic 1977 Atari 2600.

Atari Palette Python Script
Atari Palette Python Script


from math import *
from kandinsky import *
# 2020-05-28 atari 2600 colors
# kandinsky module

fill_rect(0,0,320,240,color(245,245,245))

fill_rect(15,15,55,55,color(0,0,0))
fill_rect(85,15,55,55,color(255,0,0))
fill_rect(155,15,55,55,color(255,255,0))
fill_rect(15,85,55,55,color(255,0,255))
fill_rect(155,85,55,55,color(0,255,0))
fill_rect(15,155,55,55,color(0,255,255))
fill_rect(85,155,55,55,color(0,0,255))
fill_rect(155,155,55,55,color(255,255,255))

draw_string("8",107,107)


Script:  firstdigit.py

The tenths digit from n random numbers is extracted and a bar chart is generated based on the results.  I recommend a sample size of at least 20.

firstdigit script example (sample = 100)
A Sample of 100 data points



from math import *
from random import *
from matplotlib.pyplot import *

# set up lists
x=[0,1,2,3,4,5,6,7,8,9]
y=[0,0,0,0,0,0,0,0,0,0]

# user iput
print("EWS 2020-05-29")
print("Bar Chart: First Digit")
print("Recommended at least 20")
n=int(input("n? "))

# generate list
for i in range(n):
  s=int(random()*10)
  y[s]=y[s]+1

# bar plot
h=int(n/2)
d=-int(h/4)
axis([-0.5,9.5,d,h])
bar(x,y)

# turn axis off
axis("off")

# labels at the bottom
# results at top
m=max(y)
for i in range(10):
  text(i-0.25,d+1,str(i))
  text(i-0.25,m+2,str(y[i]))
  
show()

Script:  colorfulrings.py

The script cycles through a set of nine colors, four times.   The Kandinsky module is used to generate the flowery circles as well as cycle through the colors.  This module works with integer pixels.

Color rings script in progress
Color rings script in progress


from math import *
from kandinsky import *
from time import *

# color lists
r=[255,255,255,0,0,0,51,128,255]
g=[0,102,255,128,255,0,102,128,255]
b=[0,0,0,0,0,255,255,128,255]

# angles
a=list(range(128))
for i in range(128):
  a[i]=i/128*2*pi

# draw circles
for k in range(36):
  n=int(fmod(k,9))
  for j in range(50):
    for i in range(128):
      x=int(160+(20+j)*cos(a[i]))
      y=int(120+(20+j)*sin(a[i]))
      set_pixel(x,y,color(r[n],g[n],b[n]))
  sleep(0.1)

Script:  modulusplot.py

Generate a pixel plot of the equation (x^n + y^n) mod m

Modulus Plot example, n = 3.9, m = 15.6
Input Screen  (n = 3.9, m = 15.6)

Modulus Plot result, n = 3.9, m = 15.6
Modulus Plot result, n = 3.9, m = 15.6


from math import *
from kandinsky import *
print("EWS 2020-05-28")
print("x**n + y**n mod m")
n=float(input("power? "))
m=float(input("modulus? "))

for x in range(320):
  for y in range(240):
    t=fmod(pow(x,n)+pow(y,n),m)  
    c=floor(t/m*255)
    set_pixel(x+1,y+1,color(c,c,c))


Eddie

BLOG UPDATE:
The HP Prime:  Conversion to Binary and IEEE-754 Binary blog entry that was posted on June 27, 2020 may contain errors.  In this case, I have taken that entry back to draft status and my intention is to repost the entry as soon as I can.  Apologies for any inconvenience. 

All original content copyright, © 2011-2020.  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.

Sunday, June 21, 2020

TI-84 Plus CE: Bitwise Operations

TI-84 Plus CE:  Bitwise Operations

Introduction

The programs NOT, AND, OR, and XOR are presented for the TI-84 Plus CE for integer in decimal base.

NOT

For integers x > 0, the NOT function is defined as:

Σ( 2^n * ( floor(x/2^n) mod 2 + 1 ) mod 2 ) from n = 0 to floor(log(x)/log(2))

However, observing the NOT operation on scientific calculators, the not function can  be used for integers:

-(x + 1)

TI-84 Plus CE Program NOT

"2020-05-11 EWS"
Disp "NOT(X), X>0"
Prompt X
­(X+1)→N
Disp "NOT X = ",N

Examples:

NOT 192:  Returns -193

NOT -52:  Returns 51

AND

For positive integers x, y and for x ≥ y, the AND function is defined as:

Σ( 2^n * ( [ floor(x/2^n) mod 2 ] * [ floor(y/2^n) mod 2 ] ) from n = 0 to floor(log(x)/log(2))


TI-84 Plus CE Program AND

"2020-05-11 EWS"
Disp "X AND Y, X≥Y"
Prompt X,Y
0→T
For(N,0,X-fPart(X))
(X/2^N)-fPart(X/2^N)→A
2*fPart(A/2)→A
(Y/2^N)-fPart(Y/2^N)→B
2*fPart(B/2)→B
T+2^N*A*B→T
End
Disp T

Examples:

145 AND 37:  Returns 1

226 AND 125:  Returns 96

OR

For positive integers x, y and for x ≥ y, the OR function is defined as:

Σ( 2^n *
[ [ ( floor(x/2^n) mod 2) + ( floor(y/2^n) mod 2 ) + ( floor(x/2^n) mod 2 * floor(y/2^n) mod 2) ] mod 2 ] from n = 0 to floor(log(x)/log(2))

TI-84 Plus CE Program OR

"2020-05-11 EWS"
Disp "X OR Y, X≥Y"
Prompt X,Y
0→T
For(N,0,X-fPart(X))
(X/2^N)-fPart(X/2^N)→A
2*fPart(A/2)→A
(Y/2^N)-fPart(Y/2^N)→B
2*fPart(B/2)→B
T+2^N*2*fPart((A+B+A*B)/2)→T
End
Disp T

Examples:

145 OR 37:  Returns 181

226 OR 125:  Returns 255

XOR

For positive integers x, y and for x ≥ y, the XOR function is defined as:

Σ( 2^n * [ [ floor(x/2^n) + floor(y/2^n) ] mod 2 ]  from n = 0 to floor(log(x)/log(2))

TI-84 Plus CE Program XOR

"2020-05-11 EWS"
Disp "X XOR Y, X≥Y"
Prompt X,Y
0→T
For(N,0,X-fPart(X))
(X/2^N)-fPart(X/2^N)→A
2*fPart(A/2)→A
(Y/2^N)-fPart(Y/2^N)→B
2*fPart(B/2)→B
T+2^N*2*fPart((A+B)/2)→T
End
Disp T

Examples:

145 XOR 37:  Returns 180

226 XOR 125:  Returns 159

Eddie

Source:

“Bitwise Operation”  Wikipedia.  Page last edited May 10, 2020.  Accessed on May 11, 2020.
Link:  https://en.wikipedia.org/wiki/Bitwise_operation

Eddie

All original content copyright, © 2011-2020.  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.

Saturday, June 20, 2020

HP 41C: Decimal Bitwise Operations

HP 41C: Decimal Bitwise Operations

The document covers the following operations:

NOT:  for integers
AND:  for positive integers
OR:  for positive integers
XOR:  for positive integers
Simple conversions between Binary and Decimal bases (integers up to 1023)

No extra or additional modules required.  Should work for the Swiss Micros DM41 and any emulators.

Download the PDF here: https://drive.google.com/file/d/1g7fhB4ehH0CNMizKOGpZ7bJTcLfBIVUA/view?usp=sharing

Eddie

All original content copyright, © 2011-2020.  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.

Sunday, June 14, 2020

TI-84 Plus CE: Complex Recurring Sequences

TI-84 Plus CE:  Complex Recurring Sequences

The program CMPXSEQ generates a matrix table for the complex recurring series:

C = (P + B * Q) / (1 + A)

where:
P and Q are complex constants
A = z_0
B = z_1
C = z_2

Restated, this recursion series becomes:

z_2 = (P + z_1* Q) / (1 + z_0)

In its current operating system (5.4.0), the TI-84 Plus CE's recurring sequence graphing mode cannot accept complex numbers.   Therefore a program is required.  Furthermore, matrices on the TI-84 Plus CE do not handle complex numbers.   It is required to break the complex numbers into parts.   For completeness I added both the rectangular and the polar parts of complex numbers:  real part, imaginary part, radius, and angle (dependent on angle mode).

TI-84 Plus CE Program CMPXSEQ  (text)

"EWS 2020-04-28"
ClrHome
a+bi
Disp "C=(P+B*Q)/(1+A)","COMPLEX","C=Z(N), B=Z(N-1), A=Z(N-2)"
Prompt P,Q
Input "Z0?",A
Input "Z1?",B
Input "NO OF STEPS?",N
{5,N+1}→dim([E])
For(I,0,N)
(P+Q*B)/(1+A)→C
I→[E](1,I+1)
real(C)→[E](2,I+1)
imag(C)→[E](3,I+1)
abs(C)→[E](4,I+1)
angle(C)→[E](5,I+1)
B→A
C→B
End
[E]^T→[E]
Disp "RESULT = [E]","[REAL,IMAG,ABS,ANGLE]"


Results are stored in matrix E.  ^T is the transpose function. 

Examples

Tables generated using the LibreOffice Numbers desktop app and results verified with the TI-84 Plus CE. 

Example 1:
P = 1
Q = i
z_0 = A = 2i
z_1 = B = -2



Example 2:
P = -i
Q = 1
z_0 = A = 2i
z_1 = B = -2



Example 3:
P = 1-i
Q = 1+i
z_0 = A = 2i
z_1 = B = -2



Have a great Sunday and week,

Eddie

All original content copyright, © 2011-2020.  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.

Saturday, June 13, 2020

Graph Gallery Series with GeoGebra

Graph Gallery Series with GeoGebra

The following graphs are from one to five terms of an infinite series of the form:

Σ f(n,x) from n = 0 to ∞

I use the GeoGebra online graphing tool, it is a great online, and free, graphing, mathematics, and geometry app.  Check GeoGebra out at https://www.geogebra.org

Enjoy!

Series 1: 

Σ( n * x ) from n = 0 to ∞

Σ( n * x ) from n = 0 to ∞


Series 2:

Σ( x^n * e^(-n*x) ) from n = 0 to ∞

Σ( x^n * e^(-n*x) ) from n = 0 to ∞


Series 3:

Σ( x^(-n) ) from n = 0 to ∞

Σ( x^(-n) ) from n = 0 to ∞


Series 4:

Σ( n * erf((n * x) / (n + 1)) ) from n = 0 to ∞

Σ( n * erf((n * x) / (n + 1)) ) from n = 0 to ∞


Series 5:

Σ( n * sin x + sin( x * n ) ) from n = 0 to ∞

Σ( n * sin x + sin( x * n ) ) from n = 0 to ∞


Series 6:

Σ( x^(-n) * cos( x * n ) ) from n = 0 to ∞

Σ( x^(-n) * cos( x * n ) ) from n = 0 to ∞
One of my favorite pictures.  I used this as a wallpaper on my PC.  Eddie 



Eddie

All original content copyright, © 2011-2020.  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.

Sunday, June 7, 2020

Retro Review: Radio Shack EC-4024

Retro Review: Radio Shack EC-4024

Radio Shack EC-4024 Calculator


Quick Facts:

Model:  EC-4024
Company:  Radio Shack
Equivalent of:  Casio fx-50F
Type:  Scientific 
Years:  approximately 1987 - 1995
Display:  10 digits
Batteries:  Solar 
Logic:  Algebraic (AOS)

Memory:
Registers:  7 
Constants:  9
Pre-Programmed Formulas: 23
Programming Steps: 29 between 2 slots

Features:  A Little Bit of Almost Everything

The EC-4024 has the following modes:

Mode 0:  Compute  (Main mode)
Mode 1:  Base Mode  (can be used in programs)
Mode 2:  Linear Regression (y = A + Bx) (can be used in programs)
Mode 3:  Single Deviation (one variable stats) (can be used in programs)
Mode 4:  Degrees Angle Mode
Mode 5:  Radians Angle Mode
Mode 6:  Gradians Angle Mode

Modes 7, 8, and 9:  Fixed, Scientific, and Normal (standard) display modes, respectively.

Mode . (decimal point) sets the EC-4024 in run mode while Mode EXP sets the EC-4024 in program writing mode.

The calculator handles fractions and converts results between fractions and decimal equivalents.

The base mode has the traditional four bases (binary, octal, decimal, hexadecimal integers) with Boolean algebra (OR, AND, NOT, XOR, NXOR, NEG).  

Equivalents

The Radio Shack EC-4024 is the equivalent of the Casio fx-50F calculator from the late 1980s.   There is a calculator similar to them both, which is a Casio fx-10F, however the fx-10F has an angled body and lacks the scientific constants.   

Constants

Outside of the statistics mode, the shift keys of the 1 through 9 keys holds the following constants that can be recalled (1978 Japan Industrial Standard, JIS Z-8202-1978) :

1:  C: Speed of Light:  299792458 m/s
2:  h:  Plank Constant: 6.626176 * 10^-34 J s
3:  G:  Universal Gravitational Constant: 6.672 * 10^-11 N m^2 kg^2
4:  e:  Elementary Charge:  1.6021892 * 10^-19 C 
5:  me:  Electron Mass: 9.109534 * 10^-34 kg
6:  u:  Atomic Mass Unit:  1.66055655 * 10^-27 kg
7:  Na:  Avogadro Constant: 6.022045*10^23 / mol
8:  k:  Boltzmann Constant: 1.380662 * 10^-23 J/K
9:  Vm:  Molar Value of Ideal Gas at Standard Temperature and Pressure: 0.02241383 m^3/mol

What is neat about this is that the units are listed next the constant name.  Example:  C(ms^-1) is the shift function of the 1 key.

Statistics Variables

The following are the variables used in the statistics mode.  The functions for the y values, A, B, and r are available to LR mode only.  The left parenthesis key becomes the comma key, and the right parenthesis key is the predict key (LR mode only).  

Shift 1:  average of x values
Shift 2:  population deviation of x values
Shift 3:  sample deviation of x values
Shift 4:  averages of y values
Shift 5:  population deviation of y values
Shift 6:  sample deviation of y values
Shift 7:  A:  intercept
Shift 8:  B:  slope
Shift 9:  r:   correlation
Kout 1:  Σx^2
Kout 2:  Σx
Kout 3:  n (number of data points)
Kout 4:  Σy^2
Kout 5:  Σy
Kout 6:  Σxy

Formulas

There are 23 formulas.  The character that is on the far left side of the screen prompts for the variable to be entered.   For a full list of formulas, please see the link below to download the manual.  The fx-10F manual also applies to both fx-50F and EC-4024 as well.   

Enter required values with the [RUN] key, not the [ = ] key. 

Programming

The program capacity is only 29 steps.  Thankfully, most of the shift/Kout/Mode key combinations are merged keystrokes.  For example, [MODE] [ 5 ] takes only one step, and so does [SHIFT] [ 1/x ] (for x!).  However, each press of a number key in terms of entering numbers takes a step, so to enter a numerical constant for example, 400, takes three steps ([ 4 ], [ 0 ], [ 0 ]).  With only 29 steps, economy and storing constants prior to running programs is key.  

There are a few programming tools:

x>0:  Tests whether the value in the display is positive.  If so, the program loops back to the first step in the program.

x≤M:  Tests whether the value in the display is less than or equal to the value in the M register.  If the test is true, the program loops back to the first step in the program.

ENT (the [RUN] key in write mode):  Prompts the user to enter a value.  You'll need to have a valid number entered to continue programming.

HLT (the [SHIFT] [RUN] key in write mode): Stops the calculator to show the display mid-program.  Press the [RUN] key to continue.

ALPHA (the [FMLA] key in write mode):  Prompts the user to enter a value with a prompt "A?" through "F?".   The values are stored here are stored in registers 1 through 6, respectively.

A → K1, B → K2, C → K3, D → K4, E → K5, F → K6

Sample Program:  Use the formula below to estimate gravity:

g = G * mass / radius^2 = G * A / B^2

G is the Gravitational Constant (use [SHIFT] [ 3 ])
Let A = mass
Let B = radius


Program:  P1/P2 (you designate which program area to use)

SHIFT  3    (G)
×
FMLA  a b/c  (A?)
÷
FMLA  ° ' ''  (B?)
(enter a non-zero number here, like 1)
x^2
=

Test:  Press P1/P2  

Enter 5.96E24 at the A? prompt
Enter 6.38E6 at the B? prompt

Result:  9.76924362

All programming is done blind.  The only edit function is that during programming, pressing [SHIFT] [ C ] erases the last step.

The program space can be erased by entering a number program from scratch or prior to choosing which program slot, pressing [SHIFT] [ C ].  A little confusing.  

Verdict

The keyboard is very clean and organized.  Despite the lack of steps, the EC-4024 is a great calculator and programmable scientific calculators that run on solar power are far and few between.  I was lucky to find the EC-4024 because usually fx-10F, fx-50F, and EC-4024 are either not available or command a medium to high price.

Radio Shack EC-4024 close up: Screen showing a calculation in progress


Download the manual here:  

Source:
Casio "fx-10F/fx-50F Scientific Calculator" manual.   


Eddie

All original content copyright, © 2011-2020.  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. 

Saturday, June 6, 2020

HP 42S/DM42/Free42: X-Ray Spectrometric Calculations

HP 42S/DM42/Free42:   X-Ray Spectrometric Calculations

Introduction

The program XRAY contains a menu of several calculations involving flat crystal spectronomers, which include:

[ >EW ]:  Energy wavelength conversion, where E * λ = 12.39852.  E = energy and λ = wavelength

[ →N ]:  Store n, where n is the nth crystal.   You can calculate for any crystal and have any number of crystals for this program.

[ANGLE]:  Calculates the double diffraction angle, in degrees, of any crystal given n, E, and λ by using the Bragg Equation:

θ = 2 * asin( (12.39852 * n) / (E * d) )

where d = the spacing of the crystal planes

You will be prompted for E and d each time.

[E KEV]:  Uses the Bragg Equation to calculate energy (E), given n, d, and θ.  You will be prompted for d and θ each time.

[ENRGY]:  Calculates the energy resolving power (δ) at an X-ray given its line energy (E), double refraction angle (θ), and angular divergence of the collimator (δ). 

ENERGY  = (E * 1000 * δ° * π / 180) / tan θ

Enter δ in degrees. 


HP 42S/DM42/Free42 Program: XRAY

This program is based on the HP 11C/HP 15C program as published by Török (see source)

00 { 241-Byte Prgm }
01▸LBL "XRAY"
02 DEG
03▸LBL 00
04 ">EW"
05 KEY 1 GTO 01
06 "→N"
07 KEY 2 GTO 02
08 "ANGLE"
09 KEY 3 GTO 03
10 "E KEV"
11 KEY 4 GTO 04
12 "ENRGY"
13 KEY 5 GTO 05
14 "EXIT"
15 KEY 6 GTO 06
16 MENU
17▸LBL 07
18 STOP
19 GTO 07
20▸LBL 01
21 EXITALL
22 1/X
23 12.39852
24 ×
25 STOP
26 GTO 00
27▸LBL 02
28 EXITALL
29 STO 01
30 GTO 00
31▸LBL 03
32 EXITALL
33 12.39852
34 RCL× 01
35 "E?"
36 PROMPT
37 ÷
38 "2d?"
39 PROMPT
40 ÷
41 ASIN
42 2
43 ×
44 "DBL ANGLE="
45 AVIEW
46 STOP
47 GTO 00
48▸LBL 04
49 EXITALL
50 12.39852
51 RCL× 01
52 "2d?"
53 PROMPT
54 ÷
55 "DBL ANGLE?"
56 PROMPT
57 2
58 ÷
59 SIN
60 1/X
61 ×
62 "E="
63 AVIEW
64 STOP
65 GTO 00
66▸LBL 05
67 EXITALL
68 "DBL ANGLE?"
69 PROMPT
70 2
71 ÷
72 TAN
73 1/X
74 "DELTA?"
75 PROMPT
76 →RAD
77 ×
78 "E?"
79 PROMPT
80 ×
81 1ᴇ3
82 ×
83 "ENERGY="
84 AVIEW
85 STOP
86 GTO 00
87▸LBL 06
88 CLMENU
89 EXITALL
90 .END.

You can download this program here:  https://drive.google.com/open?id=1k12l9Un9LgtrdC3139jS3SGYjNF30Qni

Note N is stored in Register R01.  Every other memory register can be used.

Example 

For a two-crystal spectrometer with properties:

Crystal 1 (n = 1):  6.285 Å (angstrom)  (d)
Crystal 2 (n = 2):  7.285 Å

Angular divergence:  0.31°   (δ)

An M_α  wave with wavelength 3.415 Å enters the system.  Find the energy of this M_α wave and the double refraction angle for each crystal.  Also was the energy-resolving power of each of the crystals.

 [ XEQ ] (XRAY)

3.415 ( >EN )     Result:  E = 3.63061 keV  (store this in R00)
[STO] 00

1st Crystal

[ R/S ] 
1 ( →N ) (ANGL)
"E?"  [RCL] 00 [R/S]
"2d?"  6.285 [R/S]

Result:  DBL ANGLE = 65.82494

(ENRGY)
"DBL ANGLE?" [ R/S ] (since θ is still on the X stack)
"DELTA?"  0.31 [STO] 02 [R/S]
"E?"  [RCL] 00 [R/S]

Result:  ENERGY= 30.34969 eV

2nd Crystal

[ R/S ] 
2 ( →N ) (ANGL)
"E?"  [RCL] 00 [R/S]
"2d?"  7.285 [R/S]

Result:  DBL ANGLE = 139.28586

(ENRGY)
"DBL ANGLE?" [ R/S ] (since θ is still on the X stack)
"DELTA?"  [RCL] 02 [R/S]
"E?"  [RCL] 00 [R/S]

Result:  ENERGY= 7.28859eV

Source:

Török, I. (1990), Line identification and other simple wavelength‐dispersive x‐ray spectrometric calculations using a pocket calculator. X‐Ray Spectrom., 19: 159-161. doi:10.1002/xrs.1300190314

Eddie

All original content copyright, © 2011-2020.  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.

Sunday, May 31, 2020

HP12C: Rational Fractions and Horner's Method

HP12C: Rational Fractions and Horner's Method

Introduction

Here are three examples on how Horner's Method can be used to quickly calculate rational fractions with polynomials.   The program code is presented for the HP 12C.

Horner's rule involves repeated factoring until the polynomial is represented as a multiplication of polynomials.  The idea is to make it easier for some scientific calculators and four-function calculators to evaluate polynomials.  Using Horner's Method for the generic cubic polynomial:

a * t^3 + b * t^2 + c * t + d
t * (a * t^2 + b * t + c) + d
t * (t * (a * t + b) + c ) + d

On an RPN keystroke calculator, such as the HP 12C a possible code would look like:

STO  t   (from the X stack)
RCL a
*
RCL b
+
RCL t
*
RCL c
+
RCL t
*
RCL d
+
RTN

For the code below, the HP 12C uses the following registers:

R0 = x

R1 = a
R2 = b
R3 = c
R4 = d
R5 = e
R6 = f
R7 = g

All but x need to be stored ahead of time before running (you can change the code to suit your needs, of course).  x is entered before pressing [ R/S ].

For all of our numerical examples, I assigned the following values:

R0 = 1.72

R1 = 6
R2 = 3
R3 = 4
R4 = 5
R5 = 3
R6 = 1
R7 = 8

Example 1

(ax + b) / (cx^2 + dx + e) = (ax + b) / (x * (cx + d) + e)

Program  (key:  key code) - 16 steps

STO 0:  44, 0
RCL 1:  45,1
  *   :  20
RCL 2:  45, 2
  +  :  40
RCL 0:  45, 0
RCL 3:  45, 3
  *  :   20
RCL 4:  45, 4
  +  :  40
RCL 0:  45, 0
  *  :  20
RCL 5:  45, 5
  +  :  40
  ÷  :  10
GTO 00:  43, 33, 00

Result with variables stored above (FIX 4):  0.5684

Example 2

(ax + b) / (cx^3 + dx^ 2 + ex + f) = (ax + b) / (x * (x * (cx + d) + e) + f)

Program  (key:  key code) - 20 steps

STO 0:  44, 0
RCL 1:  45,1
  *   :  20
RCL 2:  45, 2
  +  :  40
RCL 0:  45, 0
RCL 3:  45, 3
  *  :   20
RCL 4:  45, 4
  +  :  40
RCL 0:  45, 0
  *  :  20
RCL 5:  45, 5
  +  :  40
RCL 0:  45, 0
  *  :  20
RCL 6:  45, 6
  +  :  40
  ÷  :  10
GTO 00:  43, 33, 00

Result with variables stored above (FIX 4):  0.3225

Example 3

(ax^2 + bx + c) / (dx^3 + ex^2 + fx + g)
= (x * (ax + b) + c) / (x * (x * (dx + e) + f) + g)

Program  (key:  key code) - 24 steps

STO 0:  44, 0
RCL 1:  45,1
  *   :  20
RCL 2:  45, 2
  +  :  40
RCL 0:  45, 0
RCL 3:  45, 3
  *  :   20
RCL 4:  45, 4
  +  :  40
RCL 0:  45, 0
  *  :  20
RCL 5:  45, 5
  +  :  40
RCL 0:  45, 0
  *  :  20
RCL 6:  45, 6
  +  :  40
RCL 0:  45, 0
  *   :  20
RCL 7:  45, 7
  +  :  40
  ÷  :  10
GTO 00:  43, 33, 00

Result with variables stored above (FIX 4):  0.6111


Eddie

All original content copyright, © 2011-2020.  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.

Saturday, May 30, 2020

Retro Review: Sharp EL-506V

Retro Review:  Sharp EL-506V

Sharp EL-506V


Quick Facts

Model:  EL-506V
Company:  Sharp
Type:  Scientific
Years:  around 2003
Display:  10 digits
Batteries:  Solar (with LR-44 backup)
Original Retail Price:  Roughly $15 - $20
Logic:  Direct Algebraic Entry

Features

The Sharp EL-506V has the following modes, accessed by pressing [ 2ndF ] [ MATH ] then the appropriate number at the "0-3?" prompt:

0:  Normal (and Base Mode)
1:  Complex Number Mode
2: 3-VLE: 3 x 3 Linear Systems
3: Statistics

Entering the Statistics Mode will provide a further "0-6" prompt:
0:  SD:  Single Variable
1:  a + bx:  Linear  (y = a + bx)
2:  ...+cx²:  Quadratic  (y = a + bx + cx^2)
3:  e^x:   Exponential (y = a * exp(bx))
4:  ln x:  Logarithmic (y = a + b ln x)
5:  ax^b: Power (y = a*x^b)
6:  1/x:  Inverse (y = 1/x)

Normal Mode

Variables:

There are seven registers for the EL-506V:  A, B, C, D, X, Y, and M. The memory M has the store sum (M+) and store minus (M-) functions.  What is unusual is that there is no ALPHA key.  Instead, we will need to press [ 2ndF ] [ RCL ] to type alpha characters.

Base Conversions:

In Normal Mode, you can convert integers (fractional parts are not retained) to Hexadecimal, Octal, and Binary.   In only these three modes, you have the Boolean functions NOT, AND, OR, XOR, XNOR, and NEG. 

Calculus:

You can enact some calculus functions.  Start by typing in your function.  Don't forget to use [ 2ndF ] [ RCL] to type alpha characters. 

ALGB:  Evaluate the expression.  When the variable flashes, you are prompted for a value.

∫ dx:  Simpson's rule. Evaluates the definite integral of f(x).  You are prompted for a (lower limit), b (upper limit), and n (number of subdivisions, even).  Don't forget to enter f(x) first. 

d d/x:  Numerical Derivative of f(x).  You are prompted for a point (x) and a tolerance (dx)

Conversions and Constants:

The EL-506V has 40 conversions and constants, all which are listed on the help card that comes with the calculator. 

Fractions, decimal/degrees-minutes-seconds conversions, and random numbers complete the function set. 

Example Calculation 

Below is an example of how the display handles mathematical calculations.  Generally, numbers entered are being shown on the bottom line while everything else is shown on the top line. 


How the display operates during entering an expression

Note when editing saved expressions, everything is edited on the top line.  Inserting characters are automatic.  Delete characters by pressing [ DEL ]. 

Complex Mode

The [MATH] offers the rectangular/polar conversions.  Answers are shown in separate parts.  The real/radius part is shown first.  To see the imaginary/angle part, press [ 2nd ] [ Exp ] (←,→).

Keyboard and Verdict

I like the off-white background and how surprisingly the green, gray, and orange font shows on the calculator and keys.  It almost gives a glow-in-the-dark feel (no, the EL-506V does not glow in the dark, darn it!). 

The key response is adequate.

The calculator needs to be in total light for the display to work properly.  Maybe it just need fresh batteries, but that has been my experience so far.

This calculator is a good alternative if a modern scientific calculator is not available or you prefer a feature-rich vintage solar scientific calculator. 

Eddie

All original content copyright, © 2011-2020.  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.

Sunday, May 24, 2020

Casio Comparison: fx-9750GII vs. fx-9750GIII

Casio Comparison:  fx-9750GII vs.  fx-9750GIII

Casio claims the fx-9750GIII is comparable to the TI-84 Plus.  But what about its predecessor: fx-9750GII? 

Casio fx-9750GII full shot of the calculator
Casio fx-9750GII

Screen: Casio fx-9750GII
Screen: Casio fx-9750GII

Case and Back: Casio fx-9750GII
Case and Back: Casio fx-9750GII

Casio fx-9750GIII full shot of the calculator
Casio fx-9750GIII

Screen: Casio fx-9750GIII
Screen: Casio fx-9750GIII

Case and Back: Casio fx-9750GIII
Case and Back: Casio fx-9750GIII


In the United States, we have a new graphing calculator from Casio, the fx-9750GIII.  It is an upgrade of the fx-9750GII in several ways:

*  A new Python programming mode
*  The spreadsheet and geometry modes are added
*  Storage memory of 3 MB is allocated to hold geometry, python, and flash files.  This is an addition to the about 61K of regular memory.
*  The fx-9750GIII now has textbook input and output options.   In textbook mode, you can control whether output defaults to exact answers (fractions, square roots, terms of pi) or approximate answers.

The fx-9750GIII's case is slightly smaller than the fx-9750GII, but the width is the same.  The fx-9750GIII has a lighter body as well.  I really like the lighter feel of the fx-9750GIII.  The fx-9750GIII's back has a 3D feel to it, which is nice.  I am also impressed with the keyboard and the color contrast. 

The package I purchased did not have a USB cord.   I believe the proper cord is a mini USB cord, probably can use the cord that came with the fx-9750GII (and similar calculators) and it should be fine. 

Performance wise, the two calculators are about even, with the fx-9750GIII slightly faster. I only did a little bit of testing so far.   Neither of them are slouches. 

For a more detailed comparison, you can download a PDF comparison here:
https://drive.google.com/open?id=1bMC27Mbjw4N41qv8CZ1UD5qTJopbAVZC

(PDF document created with LibreOffice Writer)

Eddie

All original content copyright, © 2011-2020.  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.

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