Question: Let n be a positive integer. For X {0, . . . , 2^n 1}, let Y denote the integer obtained by inverting the bits

Let n be a positive integer. For X {0, . . . , 2^n 1}, let Y denote the integer obtained by inverting the bits in the n-bit, binary representation of X (note that Y {0, . . . , 2n 1}).

Show that Y + 1 -X (mod 2^n). This justifies the usual rule for computing negatives in 2s complement arithmetic.

Hint: what is X + Y ?

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