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Wouldn't you also need to keep track of the stack's size, to know if there are leading zeros?
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For trailing zeros yeah, or if you care for stack overflow/underflow. Here's a few primitives if you wanna try it out:

https://paste.sr.ht/~rabbits/cd2369cc7c72bfad0fcd83e27682095...

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Did you just explain base-2 numbers on the HN forums as if it were novel?
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I never claimed it was novel, chill.
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You missed the part where the number is being used as a 1-bit stack. They never claimed novelty, it's just a neat technique that might be unfamiliar to most people.
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It's dry humor?
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adding a zero to the left of a binary integer doesn't double it
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