Question

I know and understand the result.

For example:

<br>
 7 (decimal) = 00000111 (binary) <br>

and 7 >> 2 = 00000001 (binary) <br>
00000001 (binary) is same as 7 / 4 = 1 <br>
So 7 >> 2 = 7 / 4 <br>
<br>

But I’d like to know how this logic was created.
Can anyone elaborate on this logic?
(Maybe it just popped up in a genius’ head?)

And are there any other similar logics like this ?

Answer 1

It didn’t “pop-up” in a genius’ head. Right shifting binary numbers would divide a number by 2 and left shifting the numbers would multiply it by 2. This is because 10 is 2 in binary. Multiplying a number by 10(be it binary or decimal or hexadecimal) appends a 0 to the number(which is effectively left shifting). Similarly, dividing by 10(or 2) removes a binary digit from the number(effectively right shifting). This is how the logic really works.

There are plenty of such bit-twiddlery(a word I invented a minute ago) in computer world.

http://graphics.stanford.edu/~seander/bithacks.html Here is for the starters.

This is my favorite book: http://www.amazon.com/Hackers-Delight-Edition-Henry-Warren/dp/0321842685/ref=dp_ob_image_bk on bit-twiddlery.