Gate Logic: CAD Tools for Simplification

Implicants covered by an expanded implicant are removed from

further consideration

Quality of result depends on order of implicant expansion

Heuristic methods used to determine order

Step is called EXPAND

Irredundant cover (i.e., no proper subset is also a cover) is extracted

from the expanded primes

Just like the Quine-McCluskey Prime Implicant Chart

Step is called IRREDUNDANT COVER

Solution usually pretty good, but sometimes can be improved

Might exist another cover with fewer terms or fewer literals

Shrink prime implicants to smallest size that still covers ON-set

Step is called REDUCE

Repeat sequence REDUCE/EXPAND/IRREDUNDANT COVER to find

alternative prime implicants

Keep doing this as long as new covers improve on last solution

A number of optimizations are tried, e.g., identify and remove

essential primes early in the process