HP 15C: Digital
Root, Modulus, and 2D Coordinate Rotation
Note: steps are
for reference points only.
HP 15C: Digital Root
Input: Enter an integer and execute Label A (or whatever
label you want to assign).
Program:
Step

Key

Key Code

001

LBL A

42, 21, 11

002

ENTER

36

003

ENTER

36

004

1

1

005



30

006

9

9

007

÷

10

008

INT

43, 44

009

9

9

010

*

20

011



30

012

RTN

43, 32

Formula used:
(Define DR(n) as the digital root function)
DR(n) = n – 9 * int((n1)/9), n > 0
DR returns the sum of n’s digits and repeats until a
single digit remains.
Examples:
DR(4514) = 5
DR(9376) = 7
DR(636088) = 4
DR(761997) = 3
HP 15C: Modulus
Function
Input:
Y: A
X: B
The program calculates A mod B.
Program:
Step

Key

Key Code

001

LBL B

42, 21, 2

002

STO 2

44, 2

003

X<>Y

34

004

STO 1

44, 1

005

X<>Y

34

006

÷

10

007

FRAC

42, 44

008

RCL* 2

45, 20, 2

009

STO 3

44, 3

010

RCL 1

45, 1

011

RCL* 2

45, 20, 2

012

TEST 1 (x > 0)

43, 30, 1

013

GTO 1

22, 1

014

RCL 3

45, 3

015

RCL+ 2

45, 40, 2

016

STO 3

44, 3

017

RTN

43, 32

018

LBL 1

42, 21, 1

019

RCL 3

45, 3

020

RTN

43, 32

Formula Used:
A mod B = B * frac(A/B)
Add B to result if A*B < 0.
Registers Used:
R1 = A
R2 = B
R3 = A mod B
Examples:
A = 48, B = 3, result = 0
A = 41.3, B = 12, result = 5.3
A = 48, B = 7, result = 1
A = 50.2, B = 36, result = 21.8
HP 15C: 2D
Coordinate Rotation
Input: Store the following: X in R4, Y in R5, and θ in R3. Run the program.
Results are stored in R6 and R7, for X’ and Y’,
respectively. X’ is displayed first, press R/S to get Y’.
This program uses the Polar to Rectangular conversion.
Program:
Step

Key

Key Code

001

LBL C

42, 21, 13

002

RCL 3

45, 3

003

RCL 4

45, 4

004

>R

42, 1

005

STO 6

44, 6

006

X<>Y

34

007

STO 7

44, 7

008

RCL 3

45, 3

009

RCL 5

45, 5

010

>R

42, 1

011

RCL 7

45, 7

012

+

40

013

STO 7

44, 7

014

X<>Y

34

015

CHS

16

016

RCL 6

45, 6

017

+

40

018

STO 6

44, 6

019

R/S

31

020

X<>Y

34

021

RTN

43, 32

Formulas Used:
X’ = X * cos θ – Y * sin θ
Y’ = X * sin θ + Y * cos θ
Examples:
X (R4) = 1, Y (R5) = 2, θ (R3) = 30°. Results: X’ (R6) ≈ 0.1340, Y’ (R7) ≈ 2.2321
X (R4) = 6.45, Y (R5) = 5.25, θ (R3) = 176°. Results:
X’ (R6) ≈ 6.8005, Y’ (R7) ≈ 4.7872
Until next time, be safe everyone!
Eddie
This blog is property of Edward Shore. 2016