Chapter 1.6, Problem 10QE

a.

Explanation of Solution

Convert the base ten representation from $5$ to equivalent excess eight:

• Add $8$ to the base ten representation.

  $5+8=13$

• Convert $13$ to equivalent binary.

  $\begin{array}{c}{\left(13\right)}_{10}={\left(8+4+0+1\right)}_{10}\end{array}$

b.

Explanation of Solution

Convert the base ten representation from $-5$ to equivalent excess eight:

• Add $8$ to the base ten representation.

  $-5+8=3$

• Convert $3$ to equivalent binary.

  $\begin{array}{c}{\left(3\right)}_{10}={\left(0+0+2+1\right)}_{10}\end{array}$

c.

Explanation of Solution

Convert the base ten representation from $3$ to equivalent excess eight:

• Add $8$ to the base ten representation.

  $3+8=11$

• Convert $11$ to equivalent binary.

  $\begin{array}{c}{\left(11\right)}_{10}={\left(8+0+2+1\right)}_{10}\end{array}$

d.

Explanation of Solution

Convert the base ten representation from $0$ to equivalent excess eight:

• Add $8$ to the base ten representation.

  $0+8=8$

• Convert $8$ to equivalent binary.

  $\begin{array}{c}{\left(8\right)}_{10}={\left(8+0+0+0\right)}_{10}\\ \end{array}$

e.

Explanation of Solution

Convert the base ten representation from $7$ to equivalent excess eight:

• Add $8$ to the base ten representation.

  $7+8=15$

• Convert $15$ to equivalent binary.

  $\begin{array}{c}{\left(15\right)}_{10}={\left(8+4+2+1\right)}_{10}\end{array}$

f.

Explanation of Solution

Convert the base ten representation of $-8$ to equivalent excess eight:

• Add $8$ to the base ten representation.

  $-8+8=0$

• Convert $0$ to equivalent binary.

  $\begin{array}{c}{\left(0\right)}_{10}={\left(0+0+0+0\right)}_{10}\end{array}$