Summary: 1. Arithmetic modulo 2.
Let
b = {0, 1}.
(The b stands for bits.)
We define the binary operations + and on b by the following tables:
a b a + b
0 0 0
0 1 1
1 0 1
1 1 0
a b a b
0 0 0
0 1 0
1 0 0
1 1 1
We note that b is field with respect to these operations. One frequently writes
ab instead of a b.
We define the unary operation on b by the following table.
a a
1 0