Question 2.22: 1. Find the one’s complement of the binary number 100010. 2....

1.      The one’s complement of 100010 is found simply by inverting and is 011101.

2.      To find the two’s complement of 101101 we use the method shown in Figure 2.10:

\begin{matrix} \text{Original binary number:} \\ \text{One’s complement:} \\ \text{Adding 1:} \\ \\ \end{matrix} \begin{array}{r c}\begin{matrix} 1&0&1&1&0&1 \\ 0&1&0&0&1&0 \\ 0&0&0&0&0&1 \end{matrix}& \\ \hline \begin{matrix} 0&1&0&0&1&1 \end{matrix} \end{array}

Note that in this case there was no need to carry any digits.