Hacker's Delight

2-3. Inequalities among Logical and Arithmetic Expressions

Inequalities among binary logical expressions whose values are interpreted as unsigned integers are nearly trivial to derive. Here are two examples:

These can be derived from a list of all binary logical operations, shown in Table 2-1.

Let f(x, y) and g(x, y) represent two columns in Table 2-1. If for each row in which f(x, y) is 1, g(x, y) also is 1, then for all (x, y), Clearly, this extends to word-parallel logical operations. One can easily read off such relations (most of which are ...