On Mon, Apr 20, 2015 at 11:21 AM, Alan Gauld <alan.ga...@btinternet.com> wrote:
>>
>> B = '11011101'
>> I = 0
>> while B:
>> I = I * 2 + int(B[0])
>> B = B[1:]
>
>> Both methods work but I just can't see how the first one does.
>
> The key is that the result gets multiplied by 2 each time
> so for an N bit number the leftmost digit winds up being
> effectively 2**N, which is what you want.
The loop iterates N times, so the leftmost digit is multiplied by 2 a
total of N - 1 times, i.e. B[0] * 2 ** (N - 1).
Another way to see this is that multiplying by 2 is a bitwise left
shift. Thus you can replace the multiplication and addition with
bitwise operations as follows:
B = '11011101'
I = 0
while B:
I = (I << 1) | int(B[0], 2)
B = B[1:]
assert I == 221
Shifting the values in like this may be more intuitively obvious.
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