Bitwise: and, or, xor, nor, not

Yesterday you saw how many bits a number holds. Today you set, clear and test them one by one. You have known the instructions since week 4: and, or, xor and nor. Back then you used them with 0 and 1. In fact they work on every bit of a number separately.

Bit by bit#

and r0 %1100 %1010   # %1000 = 8
or r1 %1100 %1010    # %1110 = 14
xor r2 %1100 %1010   # %0110 = 6

Masks#

A mask is a number whose 1 bits say which places you care about. That gives four moves:

not and negative numbers#

not flips all bits. 0 does not become 1 but −1, because “all bits 1” means −1 for signed integers. 5 becomes −6. That is not a mistake: not x is always −x − 1.

not is handy for clearing masks. not mask %100 returns a number in which only bit 2 is zero. and with it clears exactly this bit, however long the number is:

not mask %100         # all bits 1 except bit 2
and value value mask    # bit 2 cleared

By the way, nor x 0 is the same as not x – both inputs 0 means 1 for nor.