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Modular arithmetic: wrapping around

Clocks don't count to 15 — they wrap back to 3. That wrap-around is exactly what the remainder operator % does, and it's the same idea behind fixed-width numbers overflowing. Watch the clock with and without it.

It's 10 o'clock. What hour shows on a 12-hour clock 5 hours later? (we want 3).

Forgetting to wrap the clock execution-derived · CPython

variables

state after line 1 runs

variable	value
`start`	`10`

step 1 / 2

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What you are looking at

Watch clock: does it keep climbing, or wrap back around 12?

Buggy — clock = start + 5 gives 15 — there's no 15 on a 12-hour clock. The code simply forgot to wrap.
Procedural — clock = (start + 5) % 12 gives 3. % takes the remainder after dividing by 12, wrapping the value back into range.

Every state you see came from running the program under CPython's tracer at build time — see how GlassBox stays honest.