• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q41E

Expert-verified Found in: Page 256 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # 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

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

See the step by step solution

## 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$-\left({2}^{4}-x\right)$.

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

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$\left({2}^{4}-1\right)=-15$.

d) Since the first bit is a 1 and the remaining bits represent the number 15 this string represents the number$\left({2}^{4}-1\right)=-15$. Note that 10000 would represent$\left({2}^{4}-0\right)=-16$, so in fact we can represent one extra negative number than positive number with this notation. ### Want to see more solutions like these? 