Cyclic K-map

A cyclic map is one where no prime implicant is essential. Every 1 is covered by at least two prime implicants, and the prime implicants link up in a ring, each overlapping the next.

The usual method stalls at step one, since there are no essential prime implicants to circle. Instead:

1. Pick any one prime implicant.
2. That choice covers some 1s and leaves neighbors that now have only one sensible group. Take those.
3. Keep going around the ring until every 1 is covered.
4. Try starting with a different prime implicant, and compare the costs.

Cyclic functions often have more than one minimal answer, each with the same number of terms and literals. Any of them is correct.

The smallest classic example is a ring of six 1s on a 3-variable map, where no group of 4 fits and every 1 sits in exactly two pairs. Larger 4-variable versions exist too. Methods like Petrick's method handle cyclic covers systematically when the map gets too big to eyeball.