Compare two integers using bit operator

Question

I need to compare two integer using Bit operator. I faced a problem where I have to compare two integers without using comparison operator.Using bit operator would help.But how?

Lets say a = 4; b = 5;

We have to show a is not equal to b. But,I would like to extend it further ,say,we will show which is greater.Here b is greater..

Answer 1

Using binary two’s complement notation

int findMax( int x, int y)
{
 int z = x - y;
 int i  = (z  >>  31)  &  0x1;
 int  max  =  x - i  *  z;
 return max;
}

Reference: Here

Answer 2

You need at least comparison to 0 and notionally this is what the CPU does for a comparison. e.g.

Equals can be modelled as ^ as the bits have to be the same to return 0

(a ^ b) == 0

if this was C you could drop the == 0 as this can be implied with

!(a ^ b)

but in Java you can't convert an int to a boolean without at least some comparison.

For comparison you usually do a subtraction, though one which handles overflows.

(long) a - b > 0 // same as a > b

subtraction is the same as adding a negative and negative is the same as ~x+1 so you can do

(long) a + ~ (long) b + 1 > 0

to drop the +1 you can change this to

(long) a + ~ (long) b >= 0 // same as a > b

You could implement + as a series of bit by bit operations with >> << & | and ^ but I wouldn't inflict that on you.