Chapter 1, Problem 34CRP

a.

Explanation of Solution

Convert $11.11$ into base ten forms:

The process of conversion of binary into base ten forms is given below:

• In the fractional binary part, the digits to the left of the decimal point represent the integer part and right to the decimal point represent the fractional part.
• The first position to the right of the decimal point is $\frac{1}{2}$.
• The first position to the left of the decimal point is $2^0$.
• Convert the number $0.11$ into base ten forms.

$\begin{array}{c}{\left(0.11\right)}_2=1\times \frac{1}{2}+1\times \frac{1}{2^2}\\ =\frac{1}{2}+\frac{1}{4}\\ =\frac{3}{4}\end{array}$

• Convert number $11$ into base ten forms

b.

Explanation of Solution

Convert $100.0101$ into base ten forms:

The process of conversion of binary into base ten forms:

• In the fractional binary part, the digits to the left of the decimal point represent the integer part and right to the decimal point represent the fractional part.
• The first position to the right of the decimal point is $\frac{1}{2}$.
• The first position to the left of the decimal point is $2^0$
• Convert the number $0.0101$ into base ten forms.

$\begin{array}{c}{\left(0.0101\right)}_2=0\times \frac{1}{2}+1\times \frac{1}{2^2}+0\times \frac{1}{2^3}+1\times \frac{1}{2^4}\\ =\frac{1}{4}+\frac{1}{16}\\ =\frac{5}{16}\end{array}$

• Convert number $100$ into base ten forms

c.

Explanation of Solution

Convert $0.1101$ into base ten forms:

The process of conversion of binary into base ten forms is given below:

• In the fractional binary part, the digits to the left of the decimal point represent the integer part and right to the decimal point represent the fractional part.
• The first position to the right of the decimal point is $\frac{1}{2}$.
• The first position to the left of the decimal point is $2^0$
• Convert number $0.1101$  into base ten form.

$\begin{array}{c}{\left(0.1101\right)}_2=1\times \frac{1}{2}+1\times \frac{1}{2^2}+0\times \frac{1}{2^3}+1\times \frac{1}{2^4}\\ =\frac{1}{2}+\end{array}$

d.

Explanation of Solution

Convert $1.0$ into base ten forms:

The process of conversion of binary into base ten forms is given below:

• In the fractional binary part, the digits to the left of the decimal point represent the integer part and right to the decimal point represent the fractional part.
• The first position to the right of the decimal point is $\frac{1}{2}$.
• The first position to the left of the decimal point is $2^0$
• Convert number 0 into base ten forms.

$\begin{array}{c}{\left(0\right)}_2=0\times \frac{1}{2}\\ =0\end{array}$

• Convert number $1$ into base ten forms

e.

Explanation of Solution

Convert $10.01$ into base ten forms:

The process of conversion of binary into base ten forms is given below:

• In the fractional binary part, the digits to the left of the decimal point represent the integer part and right to the decimal point represent the fractional part.
• The first position to the right of the decimal point is $\frac{1}{2}$.
• The first position to the left of the decimal point is $2^0$
• Convert number $.01$  into base ten forms.

$\begin{array}{c}{\left(0.01\right)}_2=0\times \frac{1}{2}+1\times \frac{1}{2^2}\\ =\frac{1}{4}\end{array}$

• Convert number $10$ into base ten forms