It's actually really simple. We'll write a and b in binary notation, for example:
a = 1001101
b = 0100111
Now what happens when you add two numbers in binary? We essentially add the numbers in each column together, and if it overflows, we carry to the next column (this is how you carry out addition in general).
So what are the columns where we need to carry, the ones that overflow? These are given by (a&b) - the columns where both a and b contain a one. To actually carry we just move everything one position to the left: ((a&b)<<1). And what are the columns where we don't need to carry, the ones that don't overflow? These are the ones where we have exactly one zero, either in a or in b, so: a^b.
In other words, a + b = ((a&b)<<1) + (a^b). To compute the average, we divide by two, or in other words, we bitshift to the right by one place: (a + b)/2 = (a&b) + ((a^b)>>1)
It's actually really simple. We'll write a and b in binary notation, for example:
Now what happens when you add two numbers in binary? We essentially add the numbers in each column together, and if it overflows, we carry to the next column (this is how you carry out addition in general).So what are the columns where we need to carry, the ones that overflow? These are given by (a&b) - the columns where both a and b contain a one. To actually carry we just move everything one position to the left: ((a&b)<<1). And what are the columns where we don't need to carry, the ones that don't overflow? These are the ones where we have exactly one zero, either in a or in b, so: a^b.
In other words, a + b = ((a&b)<<1) + (a^b). To compute the average, we divide by two, or in other words, we bitshift to the right by one place: (a + b)/2 = (a&b) + ((a^b)>>1)
If anything is unclear, feel free to ask :)