BITS.4/4.txt

Can we combine them? Smashing two objects together often produces interesting results, so lets give it a shot. Here is a representation of smashing bits together in every way possible, with ‘x’ here holding a space for the distinct names we give to exactly how we are going to smash them together.

    0    x    0    =>    ?
    0     x    1    =>    ?
    1     x    0    =>    ?
    1     x    1    =>    ?

Notice we are not necessarily commutatively smashing them in every case, saying the 0 x 1 and 0 x 1 can be distinctly different.

Given that we only have 2 symbols to work with, the ‘?’ in the above table can obviously only take one of those values. So, using our first intuition, let’s fill in the table:

    0    x    0    =>    0
    1    x    0    =>    0
    0    x    1    =>    0
    1    x    1    =>    0

or

    0    x    0    =>    1
    1    x    0    =>    1
    0    x    1    =>    1
    1    x    1    =>    1

The first, bringing all combined values to 0 and the second bringing them all to 1. Not an incredibly interesting operation, but one nonetheless, and now that we’ve found one, they should have names.

    Floor - the floor of any two bits is 0

    0    _     0    =>    0
    1    _    0    =>    0
    0    _    1    =>    0
    1    _    1    =>    1

    Ceiling - the ceiling of any two bits is 1

    0    ^    0    =>    0
    1    ^    1    =>    1
    0    ^    1    =>    1
    1    ^    1    =>    1

TOBECONTINUED