Thursday, January 7, 2016

HP 15C: Digital Root, Modulus, and 2D Coordinate Rotation

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



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