Quine–McCluskey minimization combines minterms whose binary patterns differ in exactly one position, replacing that position with a dash. Repeated combination finds prime implicants. A coverage chart then identifies essential terms. Petrick's method expresses the remaining cover choices as a Boolean product.
Worked example
Minterms 000 and 001 combine into 00-, meaning NOT A AND NOT B. For a small coverage chart, suppose required cell x is covered by P or Q, and cell y by Q or R. Petrick's expression is (P + Q)(Q + R) = Q + PR. Either choose Q alone or choose P and R.
What to watch for
Minimization depends on the cost objective. Fewest selected terms and fewest literals are related but not always the same; compare candidate covers explicitly.
Try it yourself
Can 010 and 111 combine directly in one tabulation step?
Answer: No. They differ in two positions. A direct combination requires exactly one differing bit with otherwise matching positions.
How to study this topic
Keep the original truth table beside your simplified result. Check required ones and zeros separately, and document any don't-care assumptions. A smaller expression is useful only when it still matches the specification.
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