Commodore P50 Programs

Commodore P50 Programs

A collection of programs from the vintage Commodore P50 from 1978. Check out my review from last April: https://edspi31415.blogspot.com/2025/04/spotlight-commodore-p50.html.

Air Density

This equation calculates air density, in m/kg³ given the temperature of Celsius. The standard equations are used.

ρ = p ÷ (R * (T°C + 273.15)) ≈ 359.98728 ÷ (T°C + 273.15)

p = 101,325 Pa (absolute pressure)

R = 287.05 J/(kg * K) (specific gas constant)

p/R = 101325 / 287.05 ≈ 359.98728

With limited storage space of 24 steps, the equation had to be simplified.

(The step numbers are for reference, since steps cannot be reviewed on the P50.)

Start with temperature in the display. Press GOTO 00, R/S. The air density is displayed.

00 + 01 2 02 7 03 3 04 . 05 1 06 5 07 = 08 1/x 09 × 10 3

11 5 12 2 13 . 14 9 15 8 16 7 17 2 18 8 19 = 20 r/s 21 GOTO 22 00

Examples:

Example 1: Input: 0°C, Output: 1.2922837 m/kg³

Example 2: Input: 15°C, Output: 1.2250123 m/kg³

Example 3: Input: 37.8°C, Output: 1.1351898 m/kg³

Speed of Sound

This equation calculates the speed of sound (in dry air) in m/s given the temperature of Celsius.

c_air ≈ 20.05 * √(273.15 + T°C)

Start with temperature in the display. Press GOTO 00, R/S. The speed of air is displayed.

00 + 01 2 02 7 03 3 04 . 05 1 06 5 07 = 08 √x 09 ×

10 2 11 0 12 . 13 0 14 5 15 = 16 r/s 17 GOTO 18 00

Examples:

Example 1: Input: 0°C, Output: 331.37137 m/s

Example 2: Input: 20°C, Output: 343.28856 m/s

Example 3: Input: 37.8°C, Output: 353.55718 m/s

Decibel Gain/Loss from Power Ratio

dB = 10 * log(power output ÷ power input)

Start with power output. Press GOTO 00, R/S. Then enter power input, press R/S. The decibel gain/loss is displayed.

00 ÷ 01 r/s 02 = 03 log 04 ×

05 1 06 0 07 = 08 r/s 09 GOTO 10 00

Examples:

Example 1: power output = 25 W, power input = 5 W

Input: 25 GOTO 00 r/s, 5 r/s. Output: 6.9897 dB

Example 2: power output = 30 W, power input = 42 W

Input: 30 GOTO 00 r/s, 42 r/s. Output: -1.4612804 dB

Example 3: power output = 3 W, power input = 1 W

Input: 3 GOTO 00 r/s, 1 r/s. Output: 4.7712125 dB

“Radio Mathematics” ARRL. Retrieved November 1, 2025. https://www.arrl.org/files/file/ARRL%20Handbook%20Supplemental%20Files/2023%20Edition/Radio%20Supplement.pdf

Plus or Minus Operation

This program calculates a ± b (a + b and a – b). The program leaves a – b in the display and a + b in memory, which can be toggled by the memory exchange [ x ←→ M ] key.

The program uses the memory exchange key. Enter b (the term to both be added and subtracted first), then a.

00 STO 01 r/s 02 + 03 RCL 04 = 05 r/s 06 x ←→ M 07 × 08 2 09 =

10 ± 11 + 12 RCL 13 = 14 r/s 15 GTO 16 00

Examples:

Remember, enter the second number (b) first.

Example 1: 5 ± 9

Input: 9 GOTO 00 r/s, 5, r/s. Output: 14 r/s -4

Example 2: 36 ± 20

Input: 20 GOTO 00 r/s, 36 r/s. Output: 56 r/s 16

Example 3: 310 ± 240

Input: 240 GOTO 00 r/s, 310 r/s. Output: 550 r/s 70

Combination

This is the combination function:

nCr = n! ÷ (r! * (n – r)!)

Due to only having one memory register and the factorial function does not distribute, one of the arguments (r) will need to be entered twice.

Input: n GOTO 00 r/s, r r/s, r r/s (again). Output: nCr.

00 STO 01 - 02 r/s 03 = 04 n! 05 1/x 06 × 07 RCL 08 n!

09 ÷ 10 r/s 11 n! 12 = 13 r/s 14 GOTO 15 00

Examples:

Example 1: 52 C 5

Input: 52 GOTO 00 r/s, 5 r/s, 5 r/s. Output: 2,598,960

Example 2: 34 C 12

Input: 34 GOTO 00 r/s, 12, r/s, 12 r/s. Output: 5.4835404 E 08

Example 3: 10 C 4

Input: 10 GOTO 00 r/s, 4 r/s, 4 r/s. Output: 210

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.

TI-74 and Python (Casio fx-9750GIII): Probability

TI-74 and Python (Casio fx-9750GIII):  Probability

Today's program illustrates an approach from both the BASIC and Python programming languages. 

The program offers the user to calculate common probability problems:

1)  n!:  factorial of an integer

2)  nCr:  combinations without replacement

3)  nPr:  permutations

4)  nHr:  combinations with replacement

5) bday:  probability that n people do not share a category in common from a size of categories (i.e. birthday problem:  How many people in a room don't share a birthday?)

TI-74 BASICALC Program

200 REM probability

202 INPUT "1)n! 2)nCr 3)nPr 4)nHr 5)bday "; I

204 IF I<5 THEN INPUT "n? "; N

206 IF I>1 AND I<5 THEN INPUT "r? "; R

208 ON I GOTO 220,240,260,280,300

220 X=N

222 GOSUB 320

224 PRINT "n! = "; F: PAUSE

226 GOTO 340

240 Z=1: FOR K=(N-R+1) TO N: Z=Z*K: NEXT K

242 X=R: GOSUB 320

244 Z=Z/F

246 PRINT "nCr = "; Z: PAUSE

248 GOTO 340

260 Z=1: FOR K=(N-R+1) TO N: Z=Z*K: NEXT K

262 PRINT "nPr = "; Z: PAUSE

264 GOTO 340

280 Z=1: FOR K=N TO (N+R-1): Z=Z*K: NEXT K

282 X=R: GOSUB 320: Z=Z/F

284 PRINT "nHr = "; Z: PAUSE

286 GOTO 340

300 INPUT "# categories? "; R

302 INPUT "Sample size? "; N

304 Z=1: FOR K=1 TO (N-1): Z=Z*(1-K/R): NEXT K

306 PRINT "P(all unique) = "; Z: PAUSE

308 GOTO 340

320 F=1

322 FOR K=1 TO X: F=F*K: NEXT K

324 RETURN

340 INPUT "Again? 0:No, 1:Yes "; A

342 IF A=1 THEN 202

344 IF A=0 THEN STOP

346 GOTO 340

Python Program:  prob.py 

Program completed with the Casio fx-9750GIII.

# probability

from math import *

def fact(x):

  f=1

  for k in range(1,x+1):

    f*=k    

  return f

fc=1

while fc!=0:

  print("1)n! 2)nCr")

  print("3)nPr 4)nHr")

  print("5)bday")

  ch=int(input())

  if ch<5:

    n=int(input("n? "))

  if ch>1 and ch<5:

    r=int(input("r? "))

  if ch==1:

    f=fact(n)

    print("n! = "+str(f))

  if ch==2:

    f=fact(n)/(fact(n-r)*fact(r))

    print("nCr = "+str(f))

  if ch==3:

    f=fact(n)/fact(n-r)

    print("nPr = "+str(f))

  if ch==4:

    f=fact(n+r-1)/(fact(r)*fact(n-1))

    print("nHr = "+str(f))

  if ch==5:

    r=int(input("# categories? "))

    n=int(input("Sample size? "))

    f=1

    for k in range(n):

      f*=1-k/r

    print("p(all unique)=")

    print(str(f))

  print("Again? 0)no 1)yes")

  fc=int(input())    

Examples

1) n!  

13! = 6227020800

2) nCr

n = 13, r = 6; result:  1716

3) nPr

n = 13, r = 6; result:  1235520

4) nHr

n = 13, r = 6; result:  18564

5) bday

# categories: 13

Sample size: 6

Result:  P(all unique) = .2559703523

Wishing you an excellent day.   More BASIC and Python programming coming your way tomorrow!

Eddie

All original content copyright, © 2011-2023.  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. 

HP 12C: Combination/Binomial Distribution/Negative Binomial Distribution

HP 12C:  Combination/Binomial Distribution/Negative Binomial Distribution

Introduction and Formulas

Combination: Find the number of groups out of a possible set of objects.  The order of objects obtained does not matter. 

Store n in R1, x in R0, and p in R2.  Press [ f ] [ R↓]  (CLEAR PRGM), [ R/S ]

Formula:  COMB(n, x)  = n!/(x! * (n-x)!)

Binomial Distribution:  Find number of successes (x) in a fixed number of trials (n). 

Store n in R1, x in R0, and p in R2.  Press [ g ] [ R↓ ] (GTO) 26, [R/S]

Formula:  COMB(n, x) * p^x * (1 – p)^(n – x)

Negative Binomial Distribution:  Find the number of trials (n) needed to obtain a fixed amount of successes (x).

Store x in R1, n in R0, and p in R2.  Press [ g ] [ R↓ ] (GTO) 43, [R/S]

Formula:  COMB(x – 1, n – 1) * p^(n -1) * (1 – p)^((x - 1) - (n – 1))

In the distribution calculations, p is the probability where 0 ≤ p ≤ 1. 

Note: R3 is used as a flag, which will allowed for branching.

STEP	CODE	KEY
Combination
01	0	0
02	44, 3	STO 3
03	45, 1	RCL 1
04	43, 3	N!
05	45, 0	RCL 0
06	43, 3	N!
07	10	÷
08	45, 1	RCL 1
09	45, 0	RCL 0
10	30	-
11	43, 3	N!
12	10	÷
Flag Testing
13	45, 3	RCL 3
14	1	1
15	30	-
16	43, 35	X=0
17	43, 33, 29	GTO 29
18	45, 3	RCL 3
19	2	2
20	30	-
21	43, 35	X=0
22	43, 33, 49	GTO 49
23	33	R↓
24	33	R↓
25	43, 33, 00	GTO 00
Binomial Distribution
26	1	1
27	44, 3	STO 3
28	43, 33, 03	GTO 03
29	33	R↓
30	45, 2	RCL 2
31	45, 0	RCL 0
32	21	Y^X
33	20	*
34	1	1
35	45, 2	RCL 2
36	30	-
37	45, 1	RCL 1
38	45, 0	RCL 0
39	30	-
40	21	Y^X
41	20	*
42	43, 33, 00	GTO 00
Negative Binomial Distribution
43	1	1
44	44, 30, 1	STO- 1
45	44, 30, 0	STO- 0
46	2	2
47	44, 3	STO 3
48	43, 33, 03	GTO 03
49	33	R↓
50	33	R↓
51	45, 2	RCL 2
52	45, 0	RCL 0
53	21	Y^X
54	20	*
55	1	1
56	45, 2	RCL 2
57	30	-
58	45, 1	RCL 1
59	45, 0	RCL 0
60	30	-
61	21	Y^X
62	20	*
63	43, 33, 00	GTO 00

Examples:

Find the number of combinations of groups of 2 out of possible 12 objects. 

12 [STO] 1, 2 [STO] 0, [ f ] [ R↓ ] (CLEAR PRGM)

Result:  66

Binomial Distribution:  Toss a coin 25 times. (trails) What is the probability of tossing 10 heads? (successes)  Assume a fair coin.  The variables n = 25, x = 10, p = 0.5 

25 [ STO ] 1, 10 [ STO ] 0, 0.5 [ STO ] 2, [ g ] [ R↓ ] (GTO) 26 [ R/S ]

Result:  0.10   (0.0974166393)

Negative Binomial Distribution:  Assume a fair coin. What is the probability that the 15^th tossed of heads comes on the 25^th toss of the coin?  x = 15, n = 25, p = 0.5

25 [STO] 1, 15 [STO] 0, 0.5 [ STO ] 2, [ g ] [ R↓] (GTO) 43 [ R/S ]

Result:  0.12  (0.1168999672)

This blog is property of Edward Shore, 2016.