Consider the n$-$bit binary representation of a natural number x:

the binary representation of x is $($xn$1$xn$2$ x$1$x$0)2$ x $=$

n$1$X

i$=0$

xi $2$i

where each bit xi is a binary digit, either zero or one. For example, $(00000101)2$ is the $8-$bit

binary representation of the number $5,$ since $027+026+025+024+023+122+021+120=$

$4+1=5.$ This is the format normally employed by digital computers to store nonnegative

integers.