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|.
Sometimes integers are encoded by using four-digit binary expansions to represent each decimal digit. This produces the binary coded decimal form Of the integer. For instance. 791 is encoded in this way by 011110010001. How many bits are required to represent a number with n decimal digits using this type of encoding?
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