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Q41E

Expert-verifiedFound in: Page 256

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) **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

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

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.

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