Can anyone explain why '>>2' shift means 'divided by 4' in C codes?

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

Elaborating on Aniket Inge's answer:

Number: 307₁₀ = 100110011₂

How multiply by 10 works in decimal system

10 * (307₁₀)

= 10 * (3*10² + 7*10⁰)

= 3*10²⁺¹ + 7*10⁰⁺¹

= 3*10³ + 7*10¹

= 3070₁₀

= 307₁₀ << 1

Similarly multiply by 2 in binary,

2 * (100110011₂)

= 2 * (1*2⁸ + 1*2⁵ + 1*2⁴ + 1*2¹ 1*2⁰)

= 1*2⁸⁺¹ + 1*2⁵⁺¹ + 1*2⁴⁺¹ + 1*2¹⁺¹ 1*2⁰⁺¹

= 1*2⁹ + 1*2⁶ + 1*2⁵ + 1*2² + 1*2¹

= 1001100110₂

= 100110011₂ << 1

Answer 2

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.