Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Answer Exercise 35 if each expansion is a two's complement expansion of length five.
35 What integer does each of the following one's complement representations of length five represent?
a) 11001
b) 01101
c) 10001
d) 11111

If expansion is a two’s complement expansion of length five is

a) 11001 is - 7

b) 01101 is 13

c) 10001 is - 15

d) 1111 is - 1

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1

The definition, if the first bit is a 0 then we just evaluate the binary expansion. If the first bit is a 1, then we find what number x is represented by the remaining four bits in binary; the answer is then $- (2^{4} - x)$ .

a) Since the first bit is a 1 and the remaining bits represent the number 9 this string represents the number $(2^{4} - 9) = - 7$ .

b) Since the first bit is a 0 and this is just the binary expansion of 13 the answer is 13

Step 2.

Find the following one's complement representations of length five represent.

c) Since the first bit is a 1 and the remaining bits represent the number 1 this string represents the number $(2^{4} - 1) = - 15$ .

d) Since the first bit is a 1 and the remaining bits represent the number 15 this string represents the number $(2^{4} - 1) = - 15$ . Note that 10000 would represent $(2^{4} - 0) = - 16$ , so in fact we can represent one extra negative number than positive number with this notation.

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Discrete Mathematics and its Applications

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Short Answer

Answer Exercise 35 if each expansion is a two's complement expansion of length five.
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

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Discrete Mathematics and its Applications

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Short Answer

Answer Exercise 35 if each expansion is a two's complement expansion of length five.35 What integer does each of the following one's complement representations of length five represent?a) 11001b) 01101c) 10001d) 11111

Step by Step Solution

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Answer Exercise 35 if each expansion is a two's complement expansion of length five.
35 What integer does each of the following one's complement representations of length five represent?
a) 11001
b) 01101
c) 10001
d) 11111