A five-variable K-map can be viewed as two four-variable maps, one for each value of the fifth variable. A six-variable map uses four planes arranged in Gray order. Corresponding cells in adjacent planes can be grouped, extending the same adjacency rule.
Worked example
Suppose a five-input function A, B, C, D, E equals one for every combination with E = 0. Each four-variable plane can contain the same eight qualifying cells. Grouping corresponding cells across the A planes removes A as well, leaving F = NOT E.
What to watch for
Corresponding cells are adjacent only when their plane labels differ in one bit. Large maps become hard to check by eye; tabulation or software can help verify the result.
Try it yourself
If a function's two A planes are identical, must the simplified result depend on A?
Answer: No. Matching groups across both planes eliminate A, because changing A never changes the function.
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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