Cleaner Boolean Expressions

Start Boolean cleanup with the clearest cases. If an expression repeats the same term, one copy is enough: (a & b) | (a & b) is simply a & b. Constants also have simple identities: b | 1'b0 is b, while b & 1'b1 is also b.

De Morgan’s law is another useful recognition rule. Inverting an OR is equivalent to inverting both inputs and ANDing them: ~(a | b) equals (~a) & (~b). The corresponding rule for an AND changes it into an OR of the inverted inputs.

The goal at this stage is readable, obviously equivalent logic. This course does not require Karnaugh maps or a search for the mathematically smallest possible expression.