Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

35. What integer does each of the following one’s complement representations of length five represent?
a) 11001 b) 01101 c) 10001 d) 11111

The integer have one’s complement representations of length five represent

$(a) - 6 (b) 13 (c) - 14 (d) 0$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:

(a) $11001$

The one’s complement representation starts with a 1, which indicates that the number is negative

Let us remove the first digit:

$1001$

Then replace every 1 by 0 and every 0 by 1

$0110$

Determine the corresponding integer in decimal notation:

$(0110)_{2} = {0.2}^{3} + {1.2}^{2} + 1.2 + 0 = 4 + 2 = 6$

We also knew that the integer had to be negative, thus the one’s complement $11001$ then corresponds with the integer $- 6$

Step 2:

(b) $01101$

The one’s complement representation starts with a 0, which indicates that the number is positive

Let us remove the first digit:

$1101$

Determine the corresponding integer in decimal notation:

$(1101)_{2} = {1.2}^{3} + {1.2}^{2} + 0.2 + 1 = 8 + 4 + 1 = 13$

We also knew that the integer had to be positive, thus the one’s complement $01101$ then corresponds with the integer $13$

Step 3:

$10001$

The one’s complement representation starts with a 1, which indicates that the number is negative

Let us remove the first digit:

$0001$

Then replace every 1 by 0 and every 0 by 1

$1110$

Determine the corresponding integer in decimal notation:

$(1101)_{2} = {1.2}^{3} + {1.2}^{2} + 1.2 + 1 = 8 + 4 + 2 = 14$

We also knew that the integer had to be negative, thus the one’s complement $10001$ then corresponds with the integer $- 14$

Step 4:

The one’s complement representation starts with a 1, which indicates that the number is negative

Let us remove the first digit:

$1111$

Then replace every 1 by 0 and every 0 by 1

$0000$

Determine the corresponding integer in decimal notation:

$(0000)_{2} = {0.2}^{3} + {0.2}^{2} + 0.2 + 0 = 0$

We also knew that the integer had to be negative, thus the one’s complement $11111$ then corresponds with the integer $- 0 = 0$

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Discrete Mathematics and its Applications

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Short Answer

35. What integer does each of the following one’s complement representations of length five represent?
a) 11001 b) 01101 c) 10001 d) 11111

Step by Step Solution

Step 1:

Step 2:

Step 3:

Step 4:

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Discrete Mathematics and its Applications

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Short Answer

35. What integer does each of the following one’s complement representations of length five represent? a) 11001 b) 01101 c) 10001 d) 11111

Step by Step Solution

Step 1:

Step 2:

Step 3:

Step 4:

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35. What integer does each of the following one’s complement representations of length five represent?
a) 11001 b) 01101 c) 10001 d) 11111