Reading a K-map group

Also called: reading groups, reading a group, reading K-map groups, group to product term

Turning a circled K-map group into its product term: keep each variable that stays constant across the group, and drop any variable that changes.

Every group on a K-map stands for one product term. Reading it means finding that term. The same routine works for any size, shape or position:

List the row labels and column labels the group covers.
For each variable, ask: is it the same in every cell of the group?
If it changes, drop it.
If it stays 1, write it plain. If it stays 0, write it primed.
AND the kept literals together.

Check the size: a group of 2ᵏ cells in an n-variable map keeps n − k literals. A pair in a 4-variable map must have 3 literals, a group of 4 must have 2, and so on. If the count is off, a variable was misjudged.

Why this works: within a group, each changing variable appears both as 0 and as 1 alongside every combination of the others, so it cancels by = .

When grouping 0s for a product of sums, the rule flips: a variable that stays 0 appears plain and one that stays 1 appears primed, and the literals are ORed into a sum term. See grouping zeros.

AB\CD	00	01	11	10
00	0m0	1m1	0m3	0m2
01	0m4	1m5	0m7	0m6
11	0m12	1m13	0m15	0m14
10	0m8	1m9	0m11	0m10

Worked examples

Example

A full column

Read the group in the map above: the whole column CD = 01.

1.
Rows covered: all four, so A and B both change. Drop them.
2.
Column: CD = 01, so C stays 0 and D stays 1.
3.
Term: . Four cells in a 4-variable map leave 2 literals. ✓

Example

A square split across both edges

Read the group made of the four corners, m0, m2, m8, m10.

AB\CD	00	01	11	10
00	1m0	0m1	0m3	1m2
01	0m4	0m5	0m7	0m6
11	0m12	0m13	0m15	0m14
10	1m8	0m9	0m11	1m10

1.
Rows: AB = 00 and 10 (top and bottom, which wrap). A changes; B stays 0 → .
2.
Columns: CD = 00 and 10 (left and right, which wrap). C changes; D stays 0 → .
3.
Term: .

Common mistakes

Priming the wrong way. In SOP, stayed 0 means primed and stayed 1 means plain.
Reading a label from the column's position instead of its printed bits. The third column is 11, not 10.
Keeping a variable that changes. A pair always loses exactly one variable.

Practice Reading a K-map group

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Karnaugh Maps lesson full course

And 6 more in the Karnaugh Maps lesson.

Practice exams

Learn it step by step

Reading a K-map group is taught in Karnaugh Maps.

Karnaugh Maps →

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