Bitwise operation

How are simple operations like adding and subtraction represented using only bitwise operators such as &, |, ^, >>, ~, and <<?

Also, do each of the bitwise operators perform at the same rate, or are some faster than others?

z = ((x * 0x0101010101010101ULL & 0x8040201008040201ULL) *
     0x0102040810204081ULL >> 49) & 0x5555 |
    ((y * 0x0101010101010101ULL & 0x8040201008040201ULL) *
     0x0102040810204081ULL >> 48) & 0xAAAA;

Used this snippet a couple days ago, if you know what it does from just looking at it then you know what you doing.