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# Two’s complement representations of integers are also used

ISBN: 9780073383095 37

## Solution for problem 42E Chapter 4.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 42E

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?

Step-by-Step Solution:

SOLUTIONStep 1Two compliment’s expansionStep 2Given m is a positive integer and we have to find the two’s complement representation of -m.Two’s complement representation of m represented using by n bits.

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073383095

This full solution covers the following key subjects: Answer, complement, exercise, expansions. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 42E from 4.2 chapter was answered, more than 263 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 42E from chapter: 4.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “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?” is broken down into a number of easy to follow steps, and 306 words.

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