Chapter 2, Problem 38E

a)

Program Plan Intro

Divide unsigned binary numbers:

For performing binary division, rules residing in the binary subtraction should be known. The rules are given as follows:

$\begin{array}{l}0-0=0\\ 0-1=10-1=1\\ 1-0=1\\ 1-1=\text{0}\end{array}$

Explanation of Solution

Dividing the number 101101 by 101:

Consider the two binary numbers. The dividend should be divided by the divider. The binary division for the given values is as follows:

$\begin{array}{l}\text{ 1001}\\ 101\overline{)101101}\\ \underset{\_}{\text{101}}\\ \text{ 101}\\ \underset{\_}{\text{101}}\\ \text{ x}\end{array}$

So the binary division of 101101 by 101 is $1001$.

b)

Program Plan Intro

Divide unsigned binary numbers:

For performing binary division, rules residing in the binary subtraction should be known. The rules are given as follows:

$\begin{array}{l}0-0=0\\ 0-1=10-1=1\\ 1-0=1\\ 1-1=\text{0}\end{array}$

Explanation of Solution

Dividing the number 10000001 by 101:

Consider the two binary numbers. The dividend should be divided by the divider. The binary division for the given values is as follows:

$\begin{array}{l}\text{ 11001}\text{.11001}\mathrm{....}\\ 101\overline{)10000001}\\ \underset{\_}{\text{101}}\\ \text{ 110}\\ \underset{\_}{\text{101}}\\ \text{ 1001}\\ \underset{\_}{\text{101}}\\ \text{ 1000}\\ \underset{\_}{\text{101}}\\ \text{ 110}\\ \underset{\_}{\text{101}}\\ \text{ 1001}\\ \underset{\_}{\text{101}}\\ \mathrm{....}\end{array}$

So the binary division of 10000001 by 101 is $\mathrm{11001.11001.....}$.

c)

Program Plan Intro

Divide unsigned binary numbers:

For performing binary division, rules residing in the binary subtraction should be known. The rules are given as follows:

$\begin{array}{l}0-0=0\\ 0-1=10-1=1\\ 1-0=1\\ 1-1=\text{0}\end{array}$

Explanation of Solution

Dividing the number 1001010010 by 1011:

Consider the two binary numbers. The dividend should be divided by the divider. The binary division for the given values is as follows:

$\begin{array}{l}\text{ 110110}\\ \text{1011}\overline{)\text{1001010010}}\\ \underset{\_}{\text{1011}}\\ \text{ 1111}\\ \underset{\_}{\text{1011}}\\ \text{ 10000}\\ \underset{\_}{\text{1011}}\\ \text{ 1011}\\ \underset{\_}{\text{1011}}\\ \text{ x}\end{array}$

So the binary division of 1001010010 by 1011 is $110110$.