Short Answer

37. How is the one’s complement representation of the sum of two integers obtained from the one’s complement representations of these integers?

The answer is almost, but not quite, that to obtain the one’s complement representation of the sum of two numbers, we simply add the two strings representing these numbers using Algorithm 3. Instead, after performing this operation, there may be a carry out of the left-most column; in such a case, we then add 1 more to the answer.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: We must assume that the sum actually represents a number in the appropriate range.

Assume that n bits are being used, so that numbers strictly between $- 2^{n - 1} and 2^{n - 1}$ can be represented. The answer is almost, but not quite, that to obtain the one’s complement representation of the sum of two numbers, we simply add the two strings representing these numbers using Algorithm 3. Instead, after performing this operation, there may be a carry out of the left-most column; in such a case, we then add 1 more to the answer. For example, suppose that n=4; then numbers from -7 to 7 can be represented. To add -5 and 3, we add role="math" localid="1668507124663" $1010 and 0011$ ,obtaining $1101$ ; there was no carry out of the left-most column. Since $1101$ is the one’s complement representation of -2, we have the correct answer. On the other hand, to add -4 and -3, we add $1011$ and $1100$ , obtaining 1 .The 1 $0111$ that was carried out of the left-most column is instead added to $0111$ , yielding $1000$ ,which is the one’s complement representation of-7. A proof that this method works entails considering the various cases determined by the signs and magnitudes of the addends.

Find Study Materials for

Create Study Materials

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

37. How is the one’s complement representation of the sum of two integers obtained from the one’s complement representations of these integers?

Step by Step Solution

Step 1: We must assume that the sum actually represents a number in the appropriate range.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

37. How is the one’s complement representation of the sum of two integers obtained from the one’s complement representations of these integers?

Step by Step Solution

Step 1: We must assume that the sum actually represents a number in the appropriate range.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths