A Karnaugh map arranges truth-table rows so neighboring cells differ in one input bit. Label rows and columns in Gray order. Group adjacent ones in powers of two to simplify SOP logic. The variables that change within a group disappear from its product term.
Worked example
For three inputs A, B and C, let F = Σm(0,1,4,5). These cells cover every A and C combination while B remains zero. A group of four therefore simplifies to F = NOT B. Verify the remaining four rows: each has B = 1 and output zero.
What to watch for
K-map edges wrap around. A diagonal pair is not adjacent. A four-cell group must be a valid rectangle, including wrapped rectangles.
Try it yourself
Simplify a two-input function that is one at rows 2 and 3.
Answer: Rows 10 and 11 differ only in B. A stays one, so the result is F = A.
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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