The Binary Dark Side
Define the binary dual of a base-2 number as one of the same number of digits where all the original 0 digits are 1 and all the original 1 digits are 0. (For example, the binary dual of 10110 is 01001.)
Allowing leading zeros, what's the smallest absolute difference between an 8-digit binary number and its binary dual?
The answer is 1.
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1 solution
Let a and b be 8 -bit binary duals. Then a + b = 2 5 5 by definition, and so we have a = 1 2 8 and b = 1 2 7 to have the smallest difference, which is 1