Two’s complement representations of integers also are used to simplify computer arithmetic...

Two’s complement representations of integers also are used to simplify computer arithmetic (infact, they are used much more commonly than one’s complement representations). To represent an integer x with −2n−1 ≤ x ≤ 2n−1 − 1, n bits are used.

The leftmost bit represents the sign, with a 0 used for positive integers and a 1 for negetive integers.

For a positive integer, the remaining n − 1 bits are indentical to the binary expansion of the integer. For a negetive integer, the remaining bits are the bits of the binary expasions of 2n−1 − |x|.

Show that if m is an integer with two’s complement representation an−1an−2 … a1a0,then .