Chapter 1, Problem 32CRP

a.

Explanation of Solution

Perform the addition of binary number $00101+01000$ assume the bit strings represent values in two’s complement notation:

The addition in two’s complement notation is given below:

• Binary addition is used to add binary strings of the same length.
• Add the binary number in two’s complement notation; an extra bit can be generated in the final answer on the left.
• Neglect the extra bit generated on the left of the answer.
• Add the binary number by following the above process

b.

Explanation of Solution

Perform the addition of binary number $11111+00001$ assume the bit strings represent values in two’s complement notation:

The addition in two’s complement notation is given below:

• Binary addition is used to add binary strings of the same length.
• Add the binary number in two’s complement notation; an extra bit can be generated in the final answer on the left.
• Neglect the extra bit generated on the left of the answer.
• Add the binary number by following the above process.

$\begin{array}{cccccc}& 1& 1& 1& 1& 1\end{array}$

c.

Explanation of Solution

Perform the addition of binary number $01111+00001$ assume the bit strings represent values in two’s complement notation:

The addition in two’s complement notation is given below:

• Binary addition is used to add binary strings of the same length.
• Add the binary number in two’s complement notation; an extra bit can be generated in the final answer on the left.
• Neglect the extra bit generated on the left of the answer.
• Add the binary number by following the above process.

$\begin{array}{cccccc}& 0& 1& 1& 1& 1\\ +& 0& 0& 0& 0& 1\\ & 1& 0& 0& 0& 0\end{array}$

• Convert the above answer into decimal notation by multiplying every bit of binary number to the power of two from right to left

d.

Explanation of Solution

Perform the addition of binary number $10111+11010$ assume the bit strings represent values in two’s complement notation:

The addition in two’s complement notation is given below:

• Binary addition is used to add binary strings of the same length.
• Add the binary number in two’s complement notation; an extra bit can be generated in the final answer on the left.
• Neglect the extra bit generated on the left of the answer.
• Add the binary number by following the above process.

$\begin{array}{cccccc}& 1& 0& 1& 1& 1\\ +& 1& 1& 0& 1& 0\\ 1& 1& 0& 0& 0& 1\end{array}$

• Convert the above answer into decimal notation by multiplying every bit of binary number to the power of two from right to left

e.

Explanation of Solution

Perform the addition of binary number $11111+11111$ assume the bit strings represent values in two’s complement notation:

The addition in two’s complement notation is given below:

• Binary addition is used to add binary strings of the same length.
• Add the binary number in two’s complement notation; an extra bit can be generated in the final answer on the left.
• Neglect the extra bit generated on the left of the answer.
• Add the binary number by following the above process.

$\begin{array}{cccccc}& 1& 1& 1& 1& 1\\ +& 1& 1& 1& 1& 1\\ 1& 1& 1& 1& 1& 0\end{array}$

• In the above addition, an extra bit is generated on the left of the answer that must be neglected.
• Convert the above answer into decimal notation by multiplying every bit of binary number to the power of two from right to left

f.

Explanation of Solution

Perform the addition of binary number $00111+01100$ assume the bit strings represent values in two’s complement notation:

The addition in two’s complement notation is given below:

• Binary addition is used to add binary strings of the same length.
• Add the binary number in two’s complement notation; an extra bit can be generated in the final answer on the left.
• Neglect the extra bit generated on the left of the answer.
• Add the binary number by following the above process.

$\begin{array}{cccccc}& 0& 0& 1& 1& 1\\ +& 0& 1& 1& 0& 0\\ & 1& 0& 0& 1& 1\end{array}$

• Convert the above answer into decimal notation by multiplying every bit of binary number to the power of two from right to left