Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 16 - Section 16.3 - Subtraction of Binary Numbers - Exercise - Page 554: 33

Answer

$-0 0 1 0 1 1 1 0$

Work Step by Step

$$\text{Solution}$$ Here $A = 1011101 , B = 10001011.$ Find $A - B = ?$ using 1's complement $\rightarrow$ First, find 1's complement of $B = 10001011$ $\rightarrow $ Write out the numbers as if you were subtracting decimals. $$-\begin{array}{r|r} 1011101\\ 10001011 \\ \hline \end{array}$$ $\rightarrow $ Let's use the 1's Complement Method $\rightarrow $ 1's complement of a number is obtained by subtracting all bits from $11111111$ $\rightarrow $ $\text{1's complement of 10001011 is}$ $$-\begin{array}{r|r} 1 1 1 1 1 1 1 1 \\ 1 0 0 0 1 0 1 1\\ \hline 0 1 1 1 0 1 0 0 \end{array}$$ $\rightarrow $ Now Add this 1's complement of B to A Note $\rightarrow$ Addition Rules $0 + 0 = 0$ $0 + 1 = 1$ $1 + 0 = 1$ $1 + 1 = 10$ ("$0$" in the column, carry $1$ to the next bit) So, $$+\begin{array}{r|r} 0 1 0 1 1 1 0 1\\ 0 1 1 1 0 1 0 0\\ \hline 1 1 0 1 0 0 0 1 \end{array}$$ $\rightarrow$ Here there is no carry, the answer is - (1's complement of the sum obtained 11010001) 1's complement of 11010001 is $$-\begin{array}{r|r} 1 1 1 1 1 1 1 1\\ 11010001\\ \hline 0 0 1 0 1 1 1 0 \end{array}$$ so the answer is $-0 0 1 0 1 1 1 0$
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