The MU Key on a Four Function Calculator and Programs for the DM42/HP 42S

 The MU Key on a Four Function Calculator and Programs for the DM42/HP 42S

Not too long ago, I purchased this very colorful, four function calculator from the University I work at, the Dexin BST DX-818.

The DX-818 is powered by a solar panel with an option to be run by an AAA battery when using the calculator in less than bright light conditions. The AAA battery is optional.

A Standard Calculator

This calculator is the standard four function key calculator, complete with the square root function, percent function, the standard three memory keys (M+, M-, and MRC), and a grand total (GT) key. A grand total is started when calculations are completed by pressing the equals key [ = ]. The grand total is both recalled and cleared when the [ GT ] is pressed.

The Markup Equation

Before we head to the calculators, the mark up is a calculation of between selling price (new), cost (old), and mark up. The markup is ratio between the selling price and cost over cost and as expressed as a percentage (%):

MU = (selling price – cost) ÷ cost = (selling price ÷ cost - 1)

Solving for the other variables yield:

selling price = cost * (1 + MU)

cost = selling price ÷ (1 + MU)

In these equations, MU is expressed as a decimal.

If let the selling price be the new value and cost be the old value, then we have the equation for percent change (Δ%):

Δ% = (new – old) ÷ old = (new ÷ old - 1)

Similarly:

new = old * (1 + Δ%)

old = new ÷ (1 + Δ%)

In these equations, Δ% is expressed as a decimal.

The Markup Key (MU)

On this particular calculator, there is an [ MU ] key. This is the markup key. Apparently, there are two types of [ MU ] key, one set of syntax for Casio calculators with the [ MU ] key. An example of a Casio calculator with an [ MU ] key is the MJ-120D plus. They way Casio calculators use the [ MU ] key is a calculation:

cost [ MU ] markup percentage [ % ] returns selling price.

Immediately pressing [ = ] returns selling price – cost.

However, some calculators, like the colorful calculator featured (I really wish I knew the model number) with the [ MU ] have another syntax, and that is what I will address from here on out.

On this particular calculator, the syntax, using one of the four arithmetic functions is:

y < +, -, ×, or ÷ > x [ MU ]

No use of the equals key is needed, unless you want to add the result to the grand total.

The four calculations with the [ MU ] key, on this particular calculator (and possibly the NewYes calculators from China) are:

Key Sequence	Formula Used	Notes
Y [ + ] X [ MU ]	100 * (Y ÷ X + 1)
Y [ - ] X [ MU ]	100 * (Y ÷ X - 1)	Calculates markup or percent change (Δ%). Y = selling price, new value X = cost, old value
Y [ × ] X [ MU ]	Y * (1 + X ÷ 100)	Adds X% to Y. Calculates the new value (selling price) given old value (cost) (Y) and markup (X).
Y [ ÷ ] X [ MU ]	Y ÷ (1 – X ÷ 100)	Finds the original retail price given selling price (Y) and discount rate (X). This can also be used for gross-up calculations.

Sample Calculations

Problem	Keystrokes	Result
Determine 100 * (Y ÷ X + 1) with Y = 420, X = 25	420 [ + ] 25 [ MU ]	1780
An item that cost the company $14.75 sells for $19.99. Find the markup.	19.99 [ - ] 14.75 [ MU ]	35.5254237288 (≈35.53%)
A company manufactures a product with a unit cost of $32.84 and wants a 20% markup. What is the selling price?	32.84 [ × ] 20 [ MU ]	39.408 (about $39.41)
A product is currently on sale for $39.99. If the discount is 35%, what is the original retail price.	39.99 [ ÷ ] 35 [ MU ]	61.523076923 (about $61.52)

RPN Programming with the Swiss Micros DM42

Here are four RPN programs, which are were programmed using a Swiss Micros DM42, which can be used on the HP 42S (and probably the HP 41C).

Program MU+: Y [ + ] X [ MU ]

00 {17-Byte Prgm}

01 LBL “MU+”
02 ÷

03 1

04 +

05 100

06 ×

07 RTN

08 END

Program MU-: Y [ - ] X [ MU ]

00 {17-Byte Prgm}

01 LBL “MU-”
02 ÷

03 1

04 -

05 100

06 ×

07 RTN

08 END

Program MUMLT: Y [ × ] X [ MU ]

00 {12-Byte Prgm}

01 LBL “MUMLT”
02 %

03 +

04 RTN

05 END

Program MUDIV: Y [ ÷ ] X [ MU ]

00 {21-Byte Prgm}

01 LBL “MUDIV”
02 ENTER

03 100

04 ÷

05 1

06 X<>Y

07 -

08 ÷

09 RTN

10 END

Sources

 Casio. “MJ-120D Plus” https://www.casio.com/intl/basic-calculators/product.MJ-120DPLUS/ Accessed May 23, 2026.

Eaton, Glenn. “The Calculator MU Key” Eaton Family Website. Posted on June 30, 2017. https://eatonfamily.au/calculator-mu-key/ Accessed May 23, 2026.

“How to use the MU button on a calculator? #1” YouTube Short: @newyes1162. Posted December 5, 2022. https://www.youtube.com/shorts/OiS8yFKKJSU Accessed May 23, 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.

My International Casio Collection (So Far)

 Pictured:

Pic 1:  Casio fx-991CN X (China) 

Pic 2:  Casio fx-570SPX II Iberia (Spain)

Pic 3:  Casio fx-92 Collège (France)

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: 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.

Casio fx-3650P vs. Casio fx-3650P II: Programs

Here are four programs that are done with both the fx-3650P and fx-3650P II to illustrate some programming similarities and differences.

When we start a new program with the fx-3650P II, we are prompted to the choose the appropriate mode at the beginning:

COMP (main calculation with real numbers)

CMPLX (complex numbers, primarily complex number arithmetic)

SD (single-derivation mode, single-variable statistics)

REG (regression mode, two-variable statistics)

BASE (base conversions and Boolean logic)

Left:  Casio fx-3650P (2002), Right:  fx-3650P II (2013)

Program 1: Exponential Distribution

This program calculates:

PDF: e^(-X ÷ A)

CDF (lower tail): 1 - e^(-X ÷ A)

where:

A = 1/λ parameter (i.e. average waiting time, time for an event to occur/fail/succeed)

X = time parameter

fx-3650P, 25 bytes:

? → A : ? → X :

e(-X ÷ A) ÷ A ◢

1 – e(-X ÷ A)

fx-3650P II, 25 bytes:

? → A : ? → X :

e^(-X ÷ A) ÷ A ◢

1 – e^(-X ÷ A)

Example 1:

Inputs: A = 100, X = 50

Outputs: 6.065306597E-3 (*10^-3), 0.39346934

Example 2:

Inputs: A = 50, X = 3

Outputs: 0.01883529, 0.058235466

Program 2: Using Newton’s Method to get the real root of the cubic equation that is closest to zero:

x^3 + A * x^2 + B * x + C = 0

Using Newton’s Method:

x1 = x0 – f(x0) / f’(x0) [ let y = f(x0) / f’(x0) ]

x1 = x0 - (x^3 + A * x^2 + B * x + C) / (3 * x^2 + 2 * A * x + B)

fx-3650P, 72 bytes:

? → A : ? → B : ? → C : 0 → X :

Lbl 0 :

(X³ + AX² + BX + C) ÷ (3X² + 2AX + B) → Y :

√(Y²) → D :

X – Y → X :

D ≥ 1E-8 ⇒ Goto 0 : X

√(Y²) returns Abs(Y) in Comp mode.

D is set up to be the control variable, where

D = abs((x^3 + A * x^2 + B * x + C) / (3 * x^2 + 2 * A * x + B))

fx-3650PII, 67 bytes:

? → A : ? → B : ? → C : 0 → X : 1 → Y :

While Abs(Y) ≥ 1E-8 :

(X³ + AX² + BX + C) ÷ (3X² + 2AX + B) → Y :

X – Y → X :

WhileEnd: X

We could have used the derivative function (d/dx) but typing out the derivative took less room.

Example 1: X³ + 2X² – 5X + 4 = 0

Inputs: A = 2, B = -5, C = 4

Output: -3.663076827

Example 2: X³ – 3X² + 9X + 6 = 0

Inputs: A = -3, B = 9, C = 6

Output: -0.5481911635

Program 3: Sum of the polynomial: Σ((AX + B)^C, X = 1 to Y)

fx-3650P, 57 bytes:

0 → M : ? → A : ? → B : ? → C : ? → Y : 1 → X :

Lbl 0 :

(AX + B)^C M+ : X + 1 → X : X > Y ⇒ Goto 1 : Goto 0 :

Lbl 1 : M

fx-3650PII, 41 bytes:

0 → M : ? → A : ? → B : ? → C : ? → Y : 1 → X :

For 1 → X To Y : (AX + B)^(C) M+ : Next : M

Example 1: Σ((5X – 3)^2, X = 1 to 8)

Inputs: A = 5, B = -3, C = 2, Y = 8

Output: 4092

Example 2: Σ((2X + 1)^3, X = 1 to 10)

Inputs: A = 2, B = 1, C = 3, Y = 10

Output: 29160

Program 4: Complex Roots of Unity

x^n = 1

where:

x = cos(2 * m * π / n) + i * sin(2 * m * π / n) = r * e^(2 * m * i / n)

m = 0 to n – 1, i = j = √-1

fx-3650P, 47 bytes:

Switch to complex mode. The CMPLX indicator will be displayed but not shown as a step.

Rad : ? → A : 0 → B :

Lbl 0 :

cos(2 B π ÷ A) + i × sin(2 B π ÷ A) ◢

1 + B → B : A > B ⇒ Goto 0 : 1

We must have an else condition when the jump command is used, that is why the second one is there. Also, that one “indicates” the end.

fx-3650PII, 34 bytes:

Rad : ? → A :

For 0 → B To A :

cos(2 B π ÷ A) + i × sin(2 B π ÷ A) ◢

Next : 1

The second one “indicates” the end and can be omitted.

In complex mode, the real and imaginary parts are displayed on part at a time. A settle R←→I indicator displays at the right hand side of the screen. Switch between seeing the parts by pressing [ SHIFT ] [ EXE ].

Example 1: x^3 = 1

Input: A = 3

Outputs:

1 + 0 i

-0.5 + 0.866025403 i

-0.5 - 0.866025403 i

Example 2: x^5 = 1

Input: A = 5

Outputs:

1 + 0 i

0.309016994 + 0.951056516 i

-0.809016994 + 0.587785252 i

-0.809016994 - 0.587785252 i

0.309016994 - 0.951056516 i

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: Casio fx-3650PII and Comparison with the fx-3650P and fx-50FH (II)

 Spotlight: Casio fx-3650PII and Comparison with the fx-3650P and fx-50FH (II)

Quick Facts: fx-3650P II

Model: fx-3650P II

Company: Casio

Type: Solar Scientific Algebraic, Programmable with battery backup: 1 x LR44/AP76

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

Programming Memory: 390 bytes, 4 program slots

Years in Production: 2013 (per fx-3650PII manual) to Present

Primary Market: Asia

Display: 10 digits

Casio’s fx-3650PII web page: https://www.casio.com/intl/scientific-calculators/product.FX-3650PII/

The fx-3650P II is the successor to the fx-3650P. The interface, menu structure, and the display of the fx-3650PII match that of Casio’s other current dual-powered programmable, the fx-50FH series (current as this blog entry fx-50FHII).

The modes available for the fx-3650 PII are:

COMP: This is our main calculator mode, with all the scientific functions available.

CMPLX: Complex Number mode: features complex arithmetic, conjugate, modulus (Abs), argument, rectangular/polar conversions.

BASE: Base conversions of integers between the four well known bases: binary, decimal, octal, and hexadecimal. The mode contains the standard Boolean operations.

SD: Single variable statistics (formerly named standard deviation mode)

REG: Regressions/two-variable statistics. A is usually the y-intercept and B is the slope.

The regressions available are:

Linear: y = a + b * x

Logarithmic: y = a + b * ln x

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

Power: y = a * x^b

Inverse: y = a + b / x

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

ab-Exponential: y = a * b^x

Casio fx-3650P vs Casio fx-3650P II

Both of these calculators are (or were) sold primarily in Asia.  They are dual-powered: solar with a backup battery.  

Casio fx-3650P

*  Years Released: 2002 – about 2013

*  Pressing [ e^x ] types e. e(n) takes e^n not e × n.

*  Program space: 4 programs, total of 360 bytes

*  Absolute value function (Abs) is available in complex number mode (CMPLX) mode only.

The [ MODE ] key:  

Page 1: 1: COMP, 2: CMPLX

Page 2: 1: SD, 2: REG, 3: BASE

Page 3: 1: PRGM, 2: RUN, 3: PCL

Page 4: 1: Deg, 2: Rad, 3: Grad

Page 5: 1: Fix, 2: Sci, 3: Norm

Page 6: 1: Disp (display setup, fractions, rectangular/polar in complex mode)

CMPLX (complex numbers, primarily complex number arithmetic)

SD (single-derivation mode, single-variable statistics)

REG (regression mode, two-variable statistics)

BASE (base conversions and Boolean logic)

Program Functions (P-CMD), which is a limited set:

Page 1: ? (prompt), → (store), : (separator), ◢ (output/pause)

Page 2: ⇒ (jump/if-then-else), =, ≠, >, ≥

Page 3: Goto, Lbl

To exit program editing mode, press [ MODE ], [ MODE ], select 2 for RUN

fx-3650 PII

*  Production: 2013 – current? (not in United States, but in Asia)

*  Pressing [ e^x ] types e^(. This is gives a clear indication that we are using a function (exponential).

*  Program space: 4 programs, total of 390 bytes

*  Absolute value function (Abs) is available in all modes.

The [ MODE ] key: 

Page 1: 1: COMP, 2: CMPLX, 3: BASE

Page 2: 4: SD, 5: REG, 6: PRGM

CMPLX (complex numbers, primarily complex number arithmetic)

SD (single-derivation mode, single-variable statistics)

REG (regression mode, two-variable statistics)

BASE (base conversions and Boolean logic)

The SET UP menu, use arrows to navigate:

Page 1, Angles: 1: Deg; 2: Rad; 3: Gra

Page 2, Fraction: 1: a b/c; 2: d/c

Page 3, Complex Number: 1: a+bi; 2: r∠Θ

Page 4, Statistical Frequency: 1: FreqOn; 2: FreqOff

Page 5, Contrast Setting

Operating structure has adopted the structure of the fx-50FH (a past model, it’s since been updated to the fx-50FHII).

Program Commands (P-CMD), available on both the fx-3650PII and fx-50FH series:

Page 1: ? (prompt), → (store), : (separator), ◢ (output/pause)

Page 2: ⇒ (jump/if-then-else), =, ≠

Page 3: >, <, ≥, ≤

Page 4: Goto, Lbl

Page 5: While, WhileEnd

Page 6: Next, Break

Page 7: For, To, Step

Page 8: Else, IfEnd

Page 9: If, Then

To exit program editing mode, press [ MODE ], [ MODE ], select 2 for RUN

When entering a new program, you are prompted to select the type of program at the start: COMP, CMPLX, SD, REG, or BASE.

Casio fx-3650 PII vs. Casio fx-50FH (II)

The main difference is that the fx-3650 PII has the numerical calculus functions integration and derivative, while the fx-50 FH has a library of scientific constants and 23 built in formulas. The fx-50FH has 680 bytes of programming memory.

The next post will have four programs that are done with both the fx-3650P and fx-3650P II to illustrate the programming differences.

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: Casio fx-451 Calculator

Spotlight: Casio fx-451 Calculator

Quick Facts

Model: fx-451

Company: Casio

Type: Solar Scientific Algebraic

Memory: 1 (store, recall, exchange (X←→M), sum (M+), subtract (M-))

Years in Production: 1985 to 1987 per calculator.org (https://www.calculator.org/calculators/Casio_fx-451.html)

Display: 10 digits

Casio Ledudu’s page on the fx-451: https://casio.ledudu.com/pockets.asp?lg=eng&type=1016

Folding Calculator Power

The Casio fx-451 is a folding scientific calculator. On the left side, there are the arithmetic keys, the shift, mode, and on keys, the display (10 digits), and the solar panel that operates the calculator. The right side has touch, rubber-like, membrane keys. The right side has all the scientific, statistical, fraction, base conversion, and imperial/metric conversions.

You can see my review of the fx-450 from 2018 here: https://edspi31415.blogspot.com/2018/07/retro-review-casio-fx-450-calculator.html

The available modes for the fx-451 are:

. (decimal point): SD (Standard Deviation), single variable statistics. Statistics functions are marked in blue.

0: DEC. Decimal mode. This is also the calculator’s normal/computation mode.

1: BIN. Binary integer mode (base 2). Boolean logic operators are available and are marked in green.

2: OCT. Octal integer mode (base 8). Boolean logic operators are available and are marked in green.

3: HEX. Hexadecimal integer mode (base 16). Boolean logic operators and the letter digits A-F (A=10 to F=15), are available and are marked in green.

4: DEG. Degree angle mode.

5: RAD: Radians angle mode.

6: GRA: Gradians angle mode.

7: FIX: Fixed point decimal setting

8: SCI: Scientific notion decimal setting.

9: NORM: Floating point decimal setting. Numbers less than 0.01 are shown in scientific notation form.

The engineering keys, [ENG] and [←ENG], temporarily show the number in display using scientific notation where the exponents are in multiples of 3 (i.e. 10^-6, 10^-3, 10^0, 10^3, 10^6, etc.)

Like many Casio scientific calculators, the fx-451 sports the fraction key [a b/c], allowing both entry of fractions (proper and mixed), and conversions between fractions and decimal approximations.

In addition, the fx-451 has nine scientific constants. (by pressing [SHIFT] [1-9]).  The constants are:

1. Speed of Light (c)

2. Plank’s constant (h)

3. Universal gravitational constant (G)

4. Electron charge (e)

5. Mass of an electron (me)

6. Atomic mass constant (u)

7. Avogadro’s constant (Na)

8. Boltzmann constant (k)

9. Molar volume of ideal gas (Vm)

All units are in SI units, and are listed with the constant on the keyboard.

The fx-451 Adds Imperial/Metric Conversions

(fx-450 (top), fx-451 (bottom))

The fx-451 is a later version of the fx-450 and has added a set of eight imperial/metric conversions:

Temperature: degrees Fahrenheit/Celsius

Length: inches/millimeters

Volume: gallons/liters, ounces/grams

Mass: pounds/kilograms

Energy: calories/Joules

Pressure: inches of Mercury/kilopascals, atm/megapascals

Conversions are called by the two arrow keys [ ← ] and [ → ], and are they are marked in gold. I always find conversions to be a welcome addition to any calculator.

Solar Power

Like it’s cousin, the fx-450, the fx-451 operates only by solar and light power, hence no other batteries are required.

This is a fun calculator to have, and Casio does a really good job of including lots of features even in its basic scientific calculators.

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.