[Tutor] bin to dec conversion puzzlement

[Oscar Benjamin]

On 20 April 2015 at 08:44, Jim Mooney <cybervigilante at gmail.com> wrote:
> I can't seem to get my head around this 'simple' book example of
> binary-to-decimal conversion, which goes from left to right:
>
> B = '11011101'
> I = 0
> while B:
>     I = I * 2 + int(B[0])
>     B = B[1:]


Follow through the loop and see what happens. To begin I is zero and B
is the full string. Consider B_orig to be the original string. After
the first iteration we have that
     I = B[0]   and   B = B_orig[1:]
then
     I = 2*B[0] + B[1]  and B = B_orig[2:]
then
    I = 2*(2*B[0] + B[1]) + B[2]  = 4*B[0] + 2*B[1] + B[2]
then
    I = 8*B[0] + 4*B[1] + 2*B[2] + B[3]
and eventually
    I = 128*B[0] + 64*B[1] + ... + 2*B[6] + B[7]
which is the desired result.


Oscar