Show that the integer m with one's complement

Chapter 4, Problem 39E

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Problem 39E

Show that the integer m with one's complement representation (an-1an-2…a1a2) can be found using the equation m =- an-1(2n-1 - 1) + an-22n-2+··· +a1.2+a0.

Two's complement representations of integers are also used to simplify computer arithmetic and are used more commonly than one's complement representations. To represent an integer x with -2n-1 ≤ x ≤ 2 n-1 -1 for a specified positive integer n, a total of n bits is used. The leftmost bit is used to represent the sign. A 0 bit in this position is used for positive integers, and a I bit in this position is used for negative integers. just as in one's complement expansions. For a positive integer, the remaining bits are identical to the binary expan-sion of the integer. For a negative integer, the remaining bits are the bits of the binary expansion of 2 n-1 - |x|. Two's complement expansions of integers are often used by computers because addition and subtraction of integers can be performed easily using these expansions, where these integers can be either positive or negative.