Chapter 2, Problem 34E

a)

Program Plan Intro

Subtracting signed binary numbers:

To subtract two binary signed numbers, two’s complement arithmetic method should be used. So, negative numbers are represented in two’s complement form, after that add two numbers including their sign bit. If there is any carry bit, discard the bit and take the remaining bit which gives the final result.

Some predefined rules should be followed when performing binary addition. The rules are given as follows:

$\begin{array}{l}0+0=0\\ 0+1=1\\ 1+0=1\\ 1+1=\text{0}\text{(carry 1)}\end{array}$

$\text{1+1+1}\text{= 1 (carry 1) }$

b)

Explanation of Solution

Subtracting signed binary numbers 00110101 and (-00001011):

Consider the two binary numbers. The two’s complement should be taken for signed numbers in order to perform the signed binary subtraction.

One’s complement of $(00001011)$: $11110100$

Two’s complement:

$\begin{array}{l}11110100\\ +1\\ ------\\ 1111\end{array}$

c)

Explanation of Solution

Subtracting signed binary numbers 01101111 and (-00010001):

Consider the two binary numbers. The two’s complement should be taken for signed numbers in order to perform the signed binary subtraction.

One’s complement of $(00010001)$: $11101110$

Two’s complement:

$\begin{array}{l}11101110\\ +1\\ ------\\ 1110\end{array}$