# Mod of power 2 on bitwise operators?

1. How does mod of power of 2 work on only lower order bits of a binary number (`1011000111011010`)?
2. What is this number mod 2 to power 0, 2 to power 4?
3. What does power of 2 have to do with the modulo operator? Does it hold a special property?
4. Can someone give me an example?

The instructor says "When you take something mod to power of 2 you just take its lower order bits". I was too afraid to ask what he meant =)

He meant that taking `number mod 2^n` is equivalent to stripping off all but the `n` lowest-order (right-most) bits of `number`.

For example, if n == 2,

``````number      number mod 4
00000001      00000001
00000010      00000010
00000011      00000011
00000100      00000000
00000101      00000001
00000110      00000010
00000111      00000011
00001000      00000000
00001001      00000001
etc.
``````

So in other words, `number mod 4` is the same as `number & 00000011` (where `&` means bitwise-and)

Note that this works exactly the same in base-10: `number mod 10` gives you the last digit of the number in base-10, `number mod 100` gives you the last two digits, etc.