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?

>>26
Is multiplication operator considered harmful now?
I think it's slower, it probably works like this:

  sta $4202
  lda #10
  sta $4203
  ; do something else for a while until the multiplication completes
  lda $4216