Two’s complement representations of integers are also used

Chapter 4, Problem 42E

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QUESTION:

Two’s complement representations of integers are also used to simplify computer arithmetic and are used more commonly thank one’s complement representation. To represent an integer x with 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 1 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 expansion of the integer. For a negative integer, the remaining bits are the bits of the binary expansion of . 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.Answer Exercise 36 for two's complement expansions.EXERCISE 36: One's complement representations of integers are used to simplify computer arithmetic. To represent positive and negative integers with absolute value less than 2n-1, 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 1 bit in this position is used for negative integers. For positive integers, the remaining bits are identical to the binary expansion of the integer. For negative integers, the remaining bits are obtained by first finding the binary expansion of the absolute value of the integer, and then taking the complement of each of these bits, where the complement of a 1 is a 0 and the complement of a 0 is a 1.If m is a positive integer less than 2n-1, how is the one's complement representation of -m obtained from the one's complement of m, when bit strings of length n are used?

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QUESTION:

Two’s complement representations of integers are also used to simplify computer arithmetic and are used more commonly thank one’s complement representation. To represent an integer x with 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 1 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 expansion of the integer. For a negative integer, the remaining bits are the bits of the binary expansion of . 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.Answer Exercise 36 for two's complement expansions.EXERCISE 36: One's complement representations of integers are used to simplify computer arithmetic. To represent positive and negative integers with absolute value less than 2n-1, 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 1 bit in this position is used for negative integers. For positive integers, the remaining bits are identical to the binary expansion of the integer. For negative integers, the remaining bits are obtained by first finding the binary expansion of the absolute value of the integer, and then taking the complement of each of these bits, where the complement of a 1 is a 0 and the complement of a 0 is a 1.If m is a positive integer less than 2n-1, how is the one's complement representation of -m obtained from the one's complement of m, when bit strings of length n are used?

ANSWER:

SOLUTIONStep 1Two compliment’s expansion

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