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.

RPN: Absolute Value Equations with the HP 11C and DM41X

RPN: Absolute Value Equations with the HP 11C and DM41X

Introduction: Solving |z * w + y| = x

Today’s blog focuses on solving the absolute value equation:

|z * w + y| = x

for the variable w, and the values of z, y, and x are given and are on the Classic RPN stack.

For example, in the problem |5 * w + 7| = 2, the stack would be set up as:

t: (anything, it doesn’t matter)

z: 5

y: 7

x: 2

(This is why I set the variable as w instead of the usual x.)

One approach is to use memory registers and other uses only stack operations. Today’s algorithm focuses on the latter.

Caution: In the above equation, x will always be non-negative. The equation will never be valid if x is negative.

The Algebra

Solve for w:

|z * w + y| = x

This leads us to solve the two equations:

(I)

z * w + y = -x

z * w = -x – y

w = -x/z – y/z

Let w- = -x/z – y/z = (-x/z) + (-y/z)

(II)

z * w + y = x

z * w = x – y

w = x/z - y/z

Let w+ = x/z – y/z = (x/z) + (-y/z)

Then:

w- = -x/z – y/z

w- = (-x/z) + (-y/z)

w- = (-x/z) + (-y/z) + (-x/z) + (x/z)

w- = 2 * (-x/z) + (x/z) + (-y/z)

w- = 2 * (-x/z) + w+

RPN Code: HP 11C (adoptable for other RPN calculators)

LBL A	001	42, 21, 11	Program start
R↓	002	33
R↓	003	33
X<>Y	004	34
R↓	005	33
1/x	006	15
×	007	20
LST x	008	43, 36
X<>Y	009	34
R↓	010	33
×	011	20
LST x	012	43, 36
R↑	013	43, 33
X<>Y	014	34
R↓	015	33
X<>Y	016	34
CHS	017	16
X<>Y	018	34
+	019	40
ENTER	020	36
ENTER	021	36
LST x	022	43, 36
-	023	30
LST x	024	43, 36
-	025	30
RTN	026	43, 32	Program end

RPN Code: DM41X (HP 41C series, no module is required)

LBL “ASBEQ”

RDN

RDN

X<>Y

RDN

1/x

×

LAST X

X<>Y

RDN

×

LAST X

R↑

X<>Y

RDN

X<>Y

CHS

X<>Y

+

ENTER

ENTER

LAST X

-

LAST X

-

RTN

Notes:

* RDN is shown as R↓

* To enter R↑, press XEQ, ALPHA, R, SHIFT, ENTER, ALPHA

Subroutines Used

We used several techniques to manipulate the stack. They are presented below:

Rotate stack from X, Y, Z, T to Z, X, Y, T

R↓

R↓

X<>Y

R↓

Source:

Ball, John A. Algorithms for RPN Calculators John Wiley & Sons: New York. 1978. ISBN 0-471-03070-8. pg. 78

Multiply Y and Z by 1/X. Stack: X, Y, Z, T → X, Y/X, Z/X, T

1/x

×

LAST X

X<>Y

R↓

×

LAST X

R↑

X<>Y

Change X, Y to Y+ X, Y – X

+

ENTER

ENTER

LAST X

-

LAST X

-

The resulting stack is:

z

z

y + x

y – x

Doing LAST X, -, twice is effectively subtracting whatever is in L register twice.

Examples

|4 * w – 6| = 5

Stack:

z: 4

y: -6

x: 5

Results:

y: 2.75

x: 0.25

|2 * w + 5| = 3

Stack:

z: 2

y: 5

x: 3

Results:

y: -1

x: -4

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.