Spotlight: Casio Mini CM-605

Spotlight: Casio Mini CM-605

Quick Facts

Model: CM-605

Company: Casio

Type: Four Function

Power: 4 x AA

Case: Leather Case

Memory: No memory registers

Years in Production: Starting in 1974

Display: 6 digits

Operating Mode: Chain

Shout out to Monrovia Vintage in Monrovia, California.

A Display of Six Digits (with a Surprise)

The Casio Mini (CM-605) is a vintage calculator from 1974. The calculator has the four arithmetic functions (+, -, ×, ÷). Operations are carried out as they are entered.

The zeroes in the CM-605 are shown as small zeroes. Hence, 4000 would be shown as 4ooo.

One limitation is that we can only enter numbers up to six digits. If the number is less than 1, we can only enter 5 digits after the decimal point as the leading zero is inserted automatically.

But there is a secret. It turns out that Hewlett Packard isn’t the only one to have calculators with a SHOW function. This CM-605 has a show key, [ ►], when held, it will show up to six additional digits.

From the short time that I have worked with the CM-605:

* Integers and integer parts can be shown up to 12 significant digits.

* Fractional parts can be shown up to six significant digits.

I think I can best show the power of the show key [ ► ] by a few examples:

4 ÷ 7 ≈ 0.571428

Keystrokes: [ AC ] 4 [ ÷ ] 7 [ = ]

Display: o.57142 hold [ ► ] 8ooooo

4329 × 9277 = 40160133

Keystrokes: [ AC ] 4329 [ × ] 9277 [ = ]

Display: 4o16o1 hold [ ► ] 33.oooo

5.7 ÷ 4.95 ≈ 1.15151

Keystrokes: [ AC ] 5.7 [ ÷ ] 4.95 [ = ]

Display: 1.15151 hold [ ►] oooooo

0.975 × 6.37 ÷ 8 ≈ 0.776343

Keystrokes: [ AC ] 0.975 [ × ] 6.37 [ ÷ ] 8 [ = ]

Display: o.77634 hold [ ► ] 3ooooo

Because there is no square root function, here are some mathematical constants to five digits:

ln 2 ≈ 0.69315

π ≈ 3.14159

e ≈ 2.71828

√2 ≈ 1.41421

√3 ≈ 1.73205

√5 ≈ 2.23607

Final Thoughts

I love collecting calculators made in the 1970s, especially with classic LED digits. The six-display with the show button is unique for Casio calculators. This calculator is a great showpiece.

Source

“CASIO MINI-CM-605 (A)” Casio Ledudu. June 15, 2011. https://casio.ledudu.com/pockets.asp?type=872&lg=eng Retrieved March 31, 2026.

Eddie

All original content copyright, © 2011-2026. 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.

DM41X: Interest Rate of a Forward-Forward Agreement

DM41X: Interest Rate of a Forward-Forward Agreement

A Future Interest Contract: Forward-Forward Agreement

A forward-forward agreement (yes, forward-forward is not a typo, that is what’s really called) is a financial transaction which starts on a forward date and ends on another forward date. An example transaction involves one party borrowing a sum amount to be paid back, only at the same time to deposit such amount in another short-term investment. The forward-forward rate, which I designate as FFR, is combined interest rate taking both transactions at the same time. The FFR is calculated as such:

FFR = [ (1 + IL * DL ÷ 365) ÷ (1 + IS * DS ÷ 365) – 1 ] * (365 ÷ (DL – DS))

IL: interest rate for the longer period, in decimal

DL: length of the long period

IS: interest rate for the shorter period, in decimal

DS: length of the short period

365: number of days in a year. It gets replaced with 360 if a 30/360 year is used.

If the loan lasts longer, the FFR represents the interest cost.

If the deposit lasts longer, the FFR represents the interest earned.

DM41X and HP 41C Code: FFR

01 LBL T^FFR

02 ^T FWD-FWD RATE

03 AVIEW

04 PSE

05 ^T LONG TRM DYS?

06 PROMPT

07 STO 01

08 STO 06

09 ^T LONG TRM %?

10 PROMPT

11 STO 02

12 %

13 365

14 /

15 1

16 +

17 STO 05

18 ^T SHORT TRM DYS?

19 PROMPT

20 STO 03

21 ST- 06

22 ^T SHORT TRM %?

23 PROMPT

24 STO 04

25 %

26 365

27 /

28 1

29 +

30 ST/ 05

31 RCL 05

32 1

33 -

34 365

35 *

36 RCL 06

37 /

38 2

39 10↑X

40 *

41 STO 07

42 ^T FFR=_

43 ARCL 07

44 AVIEW

45 RTN

Notes:

^T: It starts an alpha string.

Line 42: ^T FFR+_: The underscore is used as a space

Alpha strings are abbreviated in attempt for the message to fit the screen without scrolling.

Periods are assumed to be one year or less, and a 365-day year is assumed.

Examples

Example 1:

Longer Period (borrow): 49 days, 11%

Shorter Period (deposit): 30 days, 8%

Result: FFR= 15.6340

Example 2:

Longer Period (borrow): 63 days, 10.2%

Shorter Period (deposit): 31 days, 11.1%

Result: FFR= 9.2410

Source

Steiner, Bob. Mastering Financial Calculations. Second Edition. Prentice Hall: Financial Times. 2007. ISBN 978-0-273-70444-7. pp. 68-70

Eddie

All original content copyright, © 2011-2026. 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.

Numworks: Text Demos with a Poem and Rolling Screen Credits

Numworks: Text Demos with a Poem and Rolling Screen Credits 

The two scripts, which developed in Numworks:

nwtext1.py: Displaying a poem one line at a time.

nwtext2d.py: Presenting the credits in a classic TV show format.

They can be downloaded here:

https://drive.google.com/file/d/1IEDbLV4-mz9kngj0bBOkvBLrgKYg_5ha/view?usp=sharing

Display a Poem: newtext.py

Code:

# nwtext1.py

# Text Animation Demo 1

# Numworks

# Edward Shore, 2/18/2026

# import modules

from math import *

from kandinsky import *

from time import *

# Screen: 320 x 220 pixels

# list of text

t=['Roses are red','violets are blue','Nuwmorks is great','and so are you!']

# list of colors: red, violet, amber, ghost white

c=[(255,0,0),(178,0,237),(255,191,0),(245,245,245)]

# black background

fill_rect(0,0,320,220,(0,0,0))

# list the text

# each line is 20 pixels

for i in range(len(t)):

  # draw the string for each line

  # must include the black background

  # draw_string assumes white background if second color

  # is left off

  draw_string(t[i],60,60+20*i,c[i],(0,0,0))

  # time module's sleep

  sleep(1)

Notes:

1. Modules used: math, kandinsky, time. Math was entered by default every time a new script is started in Numworks. The kandinsky and time modules are specific to Numworks. The kandinsky module includes the drawing commands fill_rec and draw_string while the time module has the command sleep.

2. The line fill_rect(0,0,320,220,(0,0,0)) gives the drawing screen a black background.

3. The syntax for kandinsky’s draw_string is: draw_string(string of text, x y, text color, background color). The colors are optional, with the default set at black text color and white background. Since we have a black background for the entire screen, the background color (0,0,0) must be included.

4. To give readability I estimate that each line has a height of 20 pixels.

TV Screen Credits: nwtext2d.py

Code:

# nwtext2d.py

# Text Animation Demo 2

# Numworks

# Edward Shore, 2/19/2026

# Goal: give a classic TV style flashing of credits

# import modules

from math import *

from kandinsky import *

from time import *

# Screen: 320 x 220 pixels

# lists of text

# I'm not going to worry about center justification on this demo

# unicode for pi is u\03C0

# top line

t0=['CREDITS','Programmer','Supervisor','Directed By','Studio','Written By','A Pisces','']

# bottom line

t1=['','PI MAN','MS. SQUARE ROOT','PYTHAGOREAN THEOREM','SINE STUDIOS','PI MAN','Python Production 2026',':) \u03C0']

# black background in the loop, see comments

# roll credits

# each line is 20 pixels

for i in range(len(t0)):

  # draw a string for each line

  # text is in emerald green

  # background is black, must be included

  # since text is being replaced, we must refresh the      screen every time

  fill_rect(0,0,320,220,(0,0,0))

  draw_string(t0[i],40,60,(80,200,120),(0,0,0))

  draw_string(t1[i],40,100,(80,200,120),(0,0,0))

  # delay by 2 seconds

  sleep(2)

Notes:

1. Modules used: math, kandinsky, time. Math was entered by default every time a new script is started in Numworks. The kandinsky and time modules are specific to Numworks. The kandinsky module includes the drawing commands fill_rec and draw_string while the time module has the command sleep.

2. The line fill_rect(0,0,320,220,(0,0,0)) gives the drawing screen a black background.

3. The syntax for kandinsky’s draw_string is: draw_string(string of text, x y, text color, background color). The colors are optional, with the default set at black text color and white background. Since we have a black background for the entire screen, the background color (0,0,0) must be included.

4. In attempt to vertically center the credits, I put the top line at y = 60 and the bottom line at y = 100. In this demo, I did not worry about center justification, only choosing to left justify all the lines. The strings for the top line are stored in the list t0 while the strings for the bottom line are stored in the list t1.

I hope you enjoy these programs as I did making them,

Eddie

All original content copyright, © 2011-2026. 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.

TI-95 PROCALC Programs

TI-95 PROCALC Programs

Here’s to another year with blog! Thank you everyone for your support.

Volume and Surface Area of a Cylinder

volume = π * r^2 * h

surface area = 2 * π * r * (h + r)

Program name: CYL (064 bytes)

‘RADIUS?’ BRK STO R

x^2 * ‘HEIGHT?’ BRK STO H

* PI = STO V ‘VOL=’ COL 16 MRG V BRK

2 * PI * RCL R * (RCL R + RCL H ) = STO A

‘AREA=’ COL 16 MRG A HLT

Example:

Example 1: RADIUS = 18.88, HEIGHT = 19.09

Result: VOL= 21377.64107, AREA= 4504.249671

Example 2: RADIUS = 17, HEIGHT = 9

Result: VOL= 8171.282492, AREA= 2777.167906

Engine Displacement of a Single Cylinder (automobile engine)

displacement = π ÷ 4 * bore^2 * stroke

Program: DSP (32 bytes)

‘BORE?’ BRK x^2 *

‘STROKE?’ BRK * PI / 4 =

‘DISP=’ COL 16 MRG = HLT

Example:

Example 1: BORE = 3.5 in; STROKE = 1.9 in

Result: DISP = 18.28014225 in^3

Example 2: BORE = 3 in; STROKE = 2.4 in

Result: DISP = 16.96460033 in^3

Magnetic Force

F = I * B * L * sin(Θ)

I: current in amps

B: density in Telsa

L: length of the conductor in meters

Θ: angle of the field in degrees

F: magnetic force in Newtons

Program: MGF (32 bytes)

INV DRG ‘ANGLE?’ BRK SIN *

‘L?’ BRK * ‘B?’ BRK * ‘I?’ BRK =

‘F=’ COL 16 MRG = HLT

Examples:

Example 1: Θ: 30°, L: 1.2 m, B: 0.7 T, I: 4 A

Result: F: 1.68 N

Example 2: Θ: 24°, L: 1.8 m, B: 0.7 T, I: 4.4 A

Result: F: 2.254947949 N

Note: INV DRG sets Degree mode

Signal to Noise Ratio

This program calculates signal to noise ratio based on the units used:

Decibels: SNR = S – N

Watts: SNR = 20 * log(S ÷ N)

Voltage: SNR = 10 * log(S ÷ N)

Program: SNR (120 bytes)

‘SIGNAL-NOISE’ PAU CLR

‘S?’ BRK STO S

‘N?’ BRK STO N

‘UNITS?’

DFN F1:DB @ 01

DFN F2: W @ 02

DFN F3: V @ 03

HLT

LBL 01 RCL S – RCL N = GTL 00

LBL 02 ( RCL S / RCL N ) LOG * 20 = GTL 00

LBL 03 ( RCL S / RCL N ) LOG * 10 = GTL 00

LBL 00 ‘SNR=’ COL 16 MRG = DFN CLR HLT

Notes:

Function labels have three characters, add spaces when necessary.

The colon and at sign are added automatically.

Examples:

Example 1: S: -20 db, N: -70 db

Result: SNR = 50

Example 2: S: 128 W, N: 25 W

Result: SNR = 14.18539922

Example 3: S: 76 V, N: 3.5 V

Result: SNR = 13.36745548

Eddie

All original content copyright, © 2011-2026. 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.

Spotlight: Sharp EL-520L

 Spotlight: Sharp EL-520L

Quick Facts

Model: EL-520L

Company: Sharp

Type: Solar Scientific Algebraic

Power: Solar with battery backup, 2 x LR 44

Case: Slide case

Memory: 7 memory registers: A, B, C, D, X, Y, M (M has memory addition and subtraction)

Years in Production: 1998

Display: 2 line, with results up to 10 digits

Shout out to Spaceboy Jeffy’s Vintage Emporium from where I purchased the calculator.

Scientific Calculations in Two Lines

The Sharp EL-520L is an early two-line scientific calculator. The top line is where mathematical expressions are entered, where the bottom line is where the results are displayed.

Expressions are entered as written, as noted by Sharp’s ADVANCED D.A.L. (Direct Algebraic Logic.

Example (degrees mode, float mode):

(top | bottom)

0.5; Screen: DEG | 0.5

×; Screen: DEG 0.5*_ |

e^; Screen: DEG 0.5*e^_ |

(sin 10°); Screen: DEG 0.5*e^(sin10) |

=; Screen: DEG 0.5*e^(sin10)= | 0.594818475

Modes

The modes of the EL-520L are controlled by the MODE keys and two toggle keys:

Toggle keys:

[ DRG ]: Change mode through the degrees, radians, and grads cycle. This is how the angle mode is changed on scientific calculators from the 1980s.

[ 2ndF ] [ DRG ] ( DRG> ): A variation of angle change. In this variation, a conversion of angle measurement.

[ 2ndF ] [ . ] (FSE): This the display format toggle: Floating point (no indicator), fixed point (FIX), scientific notation (SCI), engineering notation (ENG). The TAB function, accessed by [ 2ndF ] [ +/- ], set the number of decimal points in the fixed point, scientific notation, and engineering notation format.

There is also a modify (MDF) function that internally rounds the result to the fixed decimal point settings. The modify function does not affect anything stored to variables, however. I wish there was a round function (Round(n, decimal points)) instead, to be honest.

The Mode Key:

The [ MODE ] key offers three modes:

0: Normal. Normal calculator mode.

1: STAT x: Single variable statistics. The [ STO ] key becomes the comma key and memory plus key [ M+ ] becomes the data entry key.

2: STAT xy: Linear regression mode. The data is fit to the equation y = a + bx where a is the y-intercept and b is the slope.

In the statistic modes, the variables (A -D, X, Y, M) are not operable.

Replay and Editing Keys

In Normal mode, there are three editing functions:

[ DEL ]: The standard delete character.

[ 2^nd ] [ ← ] (⟲): Takes the cursor to the beginning of the last expression

[ 2^nd ] [ → ] ( ? ): Takes the cursor to the next number after the cursor’s position

There is no insert/replace mode. It seems like Sharp was experimenting with editing commands.

Order of Operations (Quirks?)

In a lot of algebraic calculators, the square function has higher priority than negation. Entering -4² returns -16.

Implied multiplication gets a higher priority than division and regular multiplication. Therefore if we enter the infamous expression:

6÷2(1+2) returns 1 instead of 9.

This is known as PEJMDAS where J is juxtaposition, or implied multiplication. For more information, please see The How and Why of Mathematics’ video from 2019:

https://www.youtube.com/watch?v=4x-BcYCiKCk

I’ll leave the debate at this point. Of course, when it doubt, use extra parenthesis or insert an additional multiplication sign ( × ).

One quirk: To insert variables (A, B, C, D, X, Y, M) into expressions, press [ 2ndF ] [ RCL ] (ALPHA).

Final Thoughts

The Sharp EL-520L is nice, basic level calculator with the ability to enter expressions. The EL-520L has a nice amount of the features that will satisfy most needs.

Source

Flow Simulation, Ltd. “Sharp EL-520 (ADVANCED D.A.L.)” calculator.org https://www.calculator.org/calculators/Sharp_EL-520L.html

Eddie

All original content copyright, © 2011-2026. 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.

TI-84 Plus CE: Signal to Noise Ratio and Shannon’s Law

TI-84 Plus CE: Signal to Noise Ratio and Shannon’s Law

Signal to Noise Ratio (SNR)

The program SNR calculates the signal to noise ratio for inputs in one of the three units:

Decibels	S – N
Watts	20 * log( S ÷ N )
Voltage	10 * log(S ÷ N )

S: desired signal level

N: noise level

Cadence PCB Solutions (see source) provides a scale of signal to noise ratios and their effectiveness, which is summarized here:

5 dB to 10 dB	No connection is made, the ratio is too low
10 dB to 15 dB	The connection is unreliable
15 dB to 25 dB	Minimum acceptable level
25 dB to 40 dB	Good connection
41 dB and above	Excellent connection

In general, the higher the SNR, the better.

TI-84 TI-Basic Code: Signal to Noise Ratio

Program Title: SNR

Menu(“SIGNAL NOISE RATIO”,”DECIBELS”,1,”WATTS”,2,”VOLTAGE”,3)

Lbl 1

Input “SIGNAL DB? “, S

Input “NOISE DB? “, N

S – N → R

Goto 0

Lbl 2

Input “SIGNAL (W)? “, S

Input “NOISE (W)? “, N

20 * log(S / N) → R

Goto 0

Lbl 3

Input “SIGNAL (V)? “, S

Input “NOISE (W)? “, W

10 * log(S / N) → R

Goto 0

Lbl 0

Disp “SNR (DB): “, R

Examples

Example 1: S: -10 dB, N: -50 dB (from Source)

Results: 40 dB

Example 2: S: 400 W, N: 60 W

Results: 16.47817482 dB

Example 3: S: 300E-3 V (300 millivolts), N: 2E-6 V (2 microvolts)

Result: 51.76091259 dB (*source erroneously had 62 DB)

Shannon’s Law

The program SHANNON makes two calculations: signal to noise ratio in decibels and the capacity of the channel in bits per second. Shannon’s Law was discovered by Claude Shannon during World War II.

C = W * log(1 + S ÷ N) ÷ log(2)

W: bandwidth of the signal in Hertz

S: average signal received in Watts

N: average noise signal in Watts

C: maximum channel capacity in Bits per Second

TI-84 TI-Basic Code: Shannon’s Law

Program Title: SHANNON

Disp “SHANNON’S LAW”

Input “REC’D POWER (W)? “, S

Input “NOISE POWER (W)? “, N

Input “BANDWIDTH (HZ)? “, W

20 * log(S / N) → R

Disp “SIGNAL NOISE RATIO: “, R

W * log(1 + S / N) / log(2) → C

Disp “CHANNEL (BITS/S):”, C

Example

Inputs:

Average Received Signal Power (S): 49.2 W

Average Noise Power (N): 2.2 W

Bandwidth: 200 Hz

Results:

Signal Noise Ratio (SNR): 26.99084844 dB

Channel capacity: 909.2385861 bits/s

Source

Cadence. “What is Signal to Noise Ratio and How to calculate it?” Cadence PCB Solutions. 2020. Accessed November 30, 2025. https://resources.pcb.cadence.com/blog/2020-what-is-signal-to-noise-ratio-and-how-to-calculate-it

Eddie

All original content copyright, © 2011-2026. 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.