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((n-1)/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