Fun with the HP 20S (April 17, 2021 Edition)
Integer Division
The program calculates the quotient and remainder of the division:
a ÷ b
Instructions:
Enter a, press [ XEQ ] ( F ), enter b. Get the quotient, press [ R/S ], get the remainder
Program:
01 61,41,F LBL F
02 21,2 STO 2
03 45 ÷
04 26 R/S
05 21, 1 STO 1
06 74 =
07 21,0 STO 1
08 51,45 IP
09 26 R/S
10 22,0 STO 0
11 61,45 FP
12 55 ×
13 22,1 RCL 1
14 74 =
15 51,33,0 FIX 0
16 61,44 RND (round)
17 61,34 ALL
18 61,26 RTN
FIX 0, RND, ALL: round the number in the display to the nearest integer
Examples:
74 ÷ 6 = 12 R 2
Keystrokes: 74, XEQ F, 6, R/S (12) R/S (2)
1576 ÷ 237 = 6 R154
Day Number
This calculates the day number given the month and the date. A 365-day year is assumed.
Instructions:
1. Store month in memory register 1
2. Store day in memory register 2
3. Press XEQ A
Program:
01 61,41,A LBL A
02 22,1 RCL 1
03 31 INPUT
04 2 2
05 61,42 x≤y?
06 51,41,1 GTO 1
07 33 (
08 33 (
09 22,1 RCL 1
10 75 +
11 1 1
12 34 )
13 55 ×
14 3 3
15 0 0
16 73 .
17 6 6
18 34 )
19 51,45 IP
20 65 -
21 6 6
22 3 3
23 74 =
24 21,3 STO 3
25 51,41,2 GTO 2
26 61,41,1 LBL 1
27 33 (
28 33 (
29 22,1 RCL 1
30 65 -
31 1 1
32 34 )
33 55 ×
34 6 6
35 3 3
36 45 ÷
37 2 2
38 34 )
39 51,45 IP
40 74 =
41 21,3 STO 3
42 61,41,2 LBL 2
43 75 +
44 22,2 RCL 2
45 74 =
46 21,3 STO 3
47 61,26 RTN
Examples:
February 16: 2 STO 1, 16 STO 2, XEQ A. Result: 47
August 22: 8 STO 1, 22 STO 2, XEQ A. Result: 234
Source:
Duffett-Smith, Peter. Practical Astronomy With Your Calculator 2nd Ed. Cambridge University Press: Cambridge. 1979 ISBN 0-521-28411-2
Astronomy: Geocentric Parallax
The program calculates the quantities ρ sin θ' and ρ cos θ' where:
ρ = distance the observer is from the center of the Earth in meters
θ' = geocentric latitude in degrees
Inputs:
h = height of observer above sea level in meters
L = latitude of the observer in degrees, north is positive
Calculations:
h' = h / 6378140 (estimated radius of Earth is about 6,378 km)
u = atan(0.996647 tan L)
ρ sin θ' = 0.996647 sin u + h' sin L
ρ cos θ' = cos u + h' cos L
Program:
01 61,41,b LBL B
02 61,23 DEG
03 33 (
04 22,1 RCL 1
05 25 TAN
06 55 ×
07 73 .
08 9 9
09 9 9
10 6 6
11 6 6
12 4 4
13 7 7
14 21,0 STO 0
15 34 )
16 51,25 ATAN
17 21,3 STO 3
18 22,2 RCL 2
19 45 ÷
20 6 6
21 3 3
22 7 7
23 8 8
24 1 1
25 4 4
26 0 0
27 74 =
28 21,4 STO 4
29 22,0 RCL 0
30 55 ×
31 22,3 RCL 1
32 23 SIN
33 75 +
34 21,1 RCL 1
35 23 SIN
36 55 ×
37 22, 4 RCL 4
38 74 =
39 26 R/S
40 22, 3 RCL 3
41 24 COS
42 75 +
43 22, 4 RCL 4
44 55 ×
45 22, 1 RCL 1
46 24 COS
47 74 =
48 61,26 RTN
Registers used:
R1 = L (input)
R2 = h (input)
R3 = u
R4 = h / 6378140
R0 = 0.996647
Example:
Input:
L = 45.76° N
h = 53.48 m
54.76 STO 1, 53.48 STO 2, XEQ B
Result:
ρ sin θ' = .712859241, R/S
ρ cos θ' = .698873028
Source:
Duffett-Smith, Peter. Practical Astronomy With Your Calculator 2nd Ed. Cambridge University Press: Cambridge. 1979 ISBN 0-521-28411-2
