In a certain computer represents numbers in base2, if the distance between 7 and the next largest floating-point number is $2^{-12}$. What is the distance between 70 and the next largest floating number on that computer?
2026-04-13 16:00:31.1776096031
Floating point numbers
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Written in base 2, the smallest floating-point number larger than 7 is $7+2^{-12} = 111.000000000001$ (with 11 zeros). From this, you can conclude the mantissa has 15 bits, and so when we increment 70 by the smallest amount possible, we get $1000110.00000001$; this distance is $2^{-8}$.