Computer Organization and Architecture: Themes and Variations, $1^{st}.$Edition

Real computers use $8-,16-,32-,$ and $64-$bit numbers and arithmetic operations must be applied to all the bits of a word. When you add two binary words, you add pairs of bits, a column at a time, starting with the least$-$sighificant bit. Any carry$-$out is added to the next column on the left.

$\backslash$table$[[$Example $1,$Example $2,$Example $3,$Example $4],[00101010,10011111,00110011,01110011],[+01001101,+{00000001}_{?},+{11001100}_{?},+01110011]]$

When subtracting binary numbers, you have to remember that $0-1$ results in a difference $1$ and a borrow from the column on the left.

Example $1$ Example $2$ Example $3$ Example $4$ Example $5$

$\backslash$table$[[01101001,10011111,10111011,10110000,01100011],[-01001001,-01000001,-10000100,-01100011,-10110000]]$