Computer multiplication. One way to multiply two integers A times B is to add A to itself

B times. But this is rather inefficient for a large number, since, for example, to multiply

by $100$ could require $100$ separate additions. However, when expressed in binary, $100$ takes

only $7$ bits $(01100100).$ By using bit shifting $($RLF or RRF$)$ operations along with addition,

the number of iterations can be reduced, depending on the maximum sizes of the numbers

allowed in a memory unit.

The largest number one can store on our PIC$16$F$88$ is $255($all $8$ bits set to $1).$ With this

in mind, consider multiplying two $4-$bit numbers together and putting the result into an $8-$

bit register by using shifting and adding. The table below shows a multiplication of $3\backslash$times $13$

following such an algorithm where the shifts rotate through carry $($car$$ below$).$ Each row

shows the contents of C$,$ B and A at the end of each iteration, along with the operations

performed: