Chapter 2, Problem 39E

a.

Explanation of Solution

IEEE floating point representation of “3.75”:

• The decimal number “3.75” is expressed in a binary number “11.11”.

$1\times 2^1+1\times 2^0+1\times 2^{-1}+1\times 2^{-2}$

• The value after normalization is “$1$

b.

Explanation of Solution

IEEE floating point representation of “$-55\frac{23}{64}$”:

• The given number “$-\text{55}\frac{\text{23}}{\text{64}}$” is expressed in a binary number “-110111.010111”.

$1\times 2^5+1\times 2^4+0\times 2^3+1\times 2^2+1\times 2^1+1\times 2^0+0\times 2^{-1}+1\times 2^{-2}$

c.

Explanation of Solution

IEEE floating point representation of “3.1415927”:

• The given number “3.1415927” is expressed in a binary number “11.001001000011111101101”.

$\begin{array}{l}1\times 2^1+1\times 2^0+0\times 2^{-1}+0\times 2^{-2}+1\times 2^{-3}+0\times 2^{-4}+0\times 2^{-5}+1\times 2^{-6}+0\times 2^{-7}+0\times 2^{-8}\\ +0\times 2^{-9}+0\times 2^{-10}+1\times 2^{-11}+1\times 2^{}\end{array}$

d.

Explanation of Solution

IEEE floating point representation of “64000”:

• The given number “64000” is expressed in a binary number “1111101000000000”.

$\begin{array}{l}1\times 2^{15}+1\times 2^{14}+1\times 2^{13}+1\times 2^{12}+1\times 2^{11}+0\times 2^{10}+1\times 2^9+0\times 2^8+0\times 2^7+0\times 2^6\\ \end{array}$