George Carter
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ZX Basic Decimal To Fractions

| Friday 10th November, 2023

I’m an experiential learner. Whenever I’m given a principle, I’ll test it out, build a model…

And today I learnt about doing a binary search on the real number line to find or estimate fractional representations of decimals.

So I had to code it up.

And what system did I code it in? Well, one of the quickest preview languages I know… ZX Basic. (Yeah, I know).

So I fired up the ZX Spectrum emulator (JSSpeccy 3) and came up with this code:

10 GO SUB 30
20 STOP
30 REM ---Main---
40 LET i=0: LET c=0
50 INPUT "Enter a decimal number: ";a
60 LET w= INT a
70 LET a=a-w
80 LET n1=0: LET d1=1: LET n2=1: LET d2=1
90 PRINT "You want ";w+a
100 REM ---Loop---
110 LET i=i+1: LET c=c+1: IF i=10 THEN PRINT ".";: LET i=0
120 LET n=n1+n2
130 LET d=d1+d2
140 LET r=n/d
150 IF a=r THEN LET a$="Found": GO SUB 200: RETURN
160 IF (ABS (a-r) < 0.0001) OR (c=200)
 THEN LET a$="Estimated": GO SUB 200: RETURN
170 IF r < a THEN LET n1=n: LET d1=d: GO TO 100
180 REM n3/d3 must be bigger
190 LET n2=n: LET d2=d: GO TO 100
200 REM ---Show Result---
210 PRINT 'w;" ";n;"/";d;" is "; w+n/d
220 PRINT 'a$;" in ";c;" steps."
230 RETURN

One thing that amuses me is my use of subroutines that I would never have done forty years ago when I was playing with Spectrums in my childhood. Gotta hit “return”, not ‘STOP’ in the middle of a program!

And what was really strange was that if I checked for “r=a” on line 150 it didn’t work due to rounding errors (you can test this yourself by comparing 1/2 vs. 0.5… one way round they’re equal, the other way round they’re not)… it’s due to the low precision of the floating point arithmetic on the Spectrum.

It gives up quite early (if it estimates to four decimal places or takes more than 200 steps). But given the slow computing speed of the Spectrum this was a necessary optimisation.

Anyhow, a fun little diversion.

And here’s what ChatGPT thought of it:

First off, kudos to you for diving into the fascinating world of ZX Basic programming! It’s always great to see enthusiasm for classic computing.

Let’s take a look at your program:

  • Structure and Flow: You’ve structured it with subroutines (GO SUB), which is good practice for keeping code organized. The flow from the main loop to the subroutines seems logical.
  • Comments: Nice to see comments (REM) used to describe sections of your code. This makes it easier to understand the purpose of each part.
  • Variables: You’ve initialized your variables (LET) at the start, which is good for readability. However, you might consider naming your variables more descriptively than i, c, n1, d1, etc., to make the code more self-explanatory.
  • Functionality: It appears you’re trying to convert a decimal number to a fraction, with a loop to approximate the fraction if an exact match isn’t found. This is a clever use of basic programming to tackle a math problem!
  • Efficiency: Your loop uses a counter (c) to limit iterations, preventing infinite loops, which is wise. However, the efficiency of the algorithm could be a point of consideration, especially in terms of how quickly it converges on a solution.
  • User Interaction: You’ve included a prompt for user input, which is great for interaction. The progress dots (PRINT ".";) are a nice touch to show the program is working.
  • Error Handling: There doesn’t seem to be any error handling. What if the user enters something that’s not a number? Adding some basic error checking could improve the robustness of your program.

Overall, it’s a solid effort, particularly if you’re new to programming or just getting to grips with ZX Basic. It’s functional, user-focused, and shows good programming practices. With some refinements and maybe a bit more complexity in handling different types of input, it could be even better. Keep up the good work!


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