So I know what a dyadic rational is and that is represented with a finite number of binary digits in memory. The idea is that I want an explanation why is it represented in this way ? Thank you.
2026-04-03 12:50:51.1775220651
Dyadic rationals representation in the computer memory.
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The dyadic rationals consist of all rational numbers whose denominators are powers of two. These are precisely the numbers with base two expansions that terminate in a finite time. These numbers are closed under +, *, and under positive integer powers. Depending on a machine's floating-point archetecture, they can be represented exactly as as floating point numbers. There is, of course, a limit on the magnitude and the length of dyadic rationals that get represented exactly.