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

Question

I know and understand the result.

For example:

 7 (decimal) = 00000111 (binary) 


and 7 >> 2 = 00000001 (binary) 

        

Answer 1

I think you are confused by the "2" in:

7 >> 2

and are thinking it should divide by 2.

The "2" here means shift the number ("7" in this case) "2" bit positions to the right.

Shifting a number "1"bit position to the right will have the effect of dividing by 2:

8 >> 1 = 4    // In binary: (00001000) >> 1 = (00000100)

and shifting a number "2"bit positions to the right will have the effect of dividing by 4:

8 >> 2 = 2    // In binary: (00001000) >> 2 = (00000010)

Answer 2

It's because >> and << operators are shifting the binary data.

Binary value 1000 is the double  of binary value 0100
Binary value 0010 is the quarter of binary value 1000

Answer 3

Just my two cents: I did not see any mention to the fact that shifting right does not always produce the same results as dividing by 2. Since right shifting rounds toward negative infinity and integer division rounds to zero, some values (like -1 in two's complement) will just not work as expected when divided.

Answer 4

It is actually defined that way in the C standard.

From section 6.5.7:

The result of E1 >> E2 is E1 right-shifted E2 bit positions. [...] the value of the result is the integral part of the quotient of E1 / 2^E2

On most architectures, x >> 2 is only equal to x / 4 for non-negative numbers. For negative numbers, it usually rounds the opposite direction.

Compilers have always been able to optimize x / 4 into x >> 2. This technique is called "strength reduction", and even the oldest compilers can do this. So there is no benefit to writing x / 4 as x >> 2.

Answer 5

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.

Answer 6

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