Chapter 1.6, Problem 9QE

a.

Explanation of Solution

Convert the excess eight representation of $1110$ to equivalent base ten:

• Convert $1110$ to decimal representation.

  $\begin{array}{c}{\left(1110\right)}_2={(1\times 2^3+1\times 2^2+1\times {}^{}}_{}\end{array}$

b.

Explanation of Solution

Convert the excess eight representation of $0111$ to equivalent base ten:

• Convert $0111$ to decimal representation.

  $\begin{array}{c}{\left(0111\right)}_2={(0\times 2^3+1\times 2^2+1\times 2^1}_{}\end{array}$

c.

Explanation of Solution

Convert the excess eight representation of $1000$ to equivalent base ten:

• Convert $1000$ to decimal representation.

  $\begin{array}{c}{\left(1000\right)}_2={(1\times 2^3+0\times 2^2+0\times }_{}\end{array}$

d.

Explanation of Solution

Convert the excess eight representation of $0010$ to equivalent base ten.

• Convert $0010$ to decimal representation.

  $\begin{array}{c}{\left(0010\right)}_2={(0\times 2^3+0\times 2^2+1\times 2^1}_{}\end{array}$

e.

Explanation of Solution

Convert the excess eight representation of $0000$ to equivalent base ten.

• Convert $0000$ to decimal representation.

  $\begin{array}{c}{\left(0000\right)}_2={(0\times 2^3+0\times 2^2+0\times 2^1}_{}\end{array}$

f.

Explanation of Solution

Convert the excess eight representation of $1001$ to equivalent base ten.

• Convert $1001$ to decimal representation.

  $\begin{array}{c}{\left(1001\right)}_2={(1\times 2^3+0\times 2^2+0\times }_{}\end{array}$