Chapter 1.6, Problem 7QE

a.

Explanation of Solution

Solve $6-\left(-1\right)$ in two’s compliment notation and verify the answers:

• Add the two numbers as:

  $\begin{array}{c}6-\left(-1\right)=6+1\\ =7\end{array}$

• Convert the notation in two’s compliment:

  $\begin{array}{l}0110\\ \frac{+0001}{0111}\end{array}$

• Convert

b.

Explanation of Solution

Solve $3-\left(-2\right)$ in two’s compliment notation and verify the answers:

• Add the two numbers as:

  $\begin{array}{c}3-\left(-2\right)=3+2\\ =5\end{array}$

• Convert the notation in two’s compliment:

  $\begin{array}{l}0011\\ \frac{+0010}{0101}\end{array}$

• Convert

c.

Explanation of Solution

Solve $4-6$ in two’s compliment notation and verify the answers:

• Add the two numbers as:

  $4-6=-2$

• Convert the notation in two’s compliment:

  $\begin{array}{l}0100\\ \frac{+1010}{1110}\end{array}$

• Since the obtained number is negative, take the two’s compliment of $1110$.

  $\begin{array}{c}{\left(1110\right)}_2=\left(0001+1\right)\\ =(\end{array}$

d.

Explanation of Solution

Solve $2-\left(-4\right)$ in two’s compliment notation and verify the answers:

• Add the two numbers as:

  $\begin{array}{c}2-\left(-4\right)=2+4\\ =6\end{array}$

• Convert the notation in two’s compliment:

  $\begin{array}{l}0010\\ \frac{+0100}{0110}\end{array}$

• Convert

e.

Explanation of Solution

Solve $1-5$ in two’s compliment notation and verify the answers:

• Add the two numbers as:

  $1-5=-4$

• Convert the notation in two’s compliment:

  $\begin{array}{l}0001\\ \frac{+1011}{1100}\end{array}$

• Since the obtained number is negative, take the two’s compliment of $1100$.

  $\begin{array}{c}{\left(1100\right)}_2={\left(0011+1\right)}_2\\ ={(}_{}\end{array}$