Simplify the following Boolean expression using 4-variables K-map.
F(A, B, C, D) = Σ m(3, 6, 7, 11, 12, 13, 14, 15)

Explanation

Plotting the eight minterms 3, 6, 7, 11, 12, 13, 14 and 15 on a 4-variable K-map (rows AB, columns CD, both in Gray-code order) gives three groups of four adjacent 1s: the whole column CD = 11 (cells 3, 7, 11, 15) gives the term CD; the whole row AB = 11 (cells 12, 13, 14, 15) gives the term AB; and the 2×2 block formed by AB ∈ {01, 11} and CD ∈ {10, 11} (cells 6, 7, 14, 15) gives the term BC. Together CD, AB and BC cover exactly these eight minterms with no extra 1s included, and none of the three groups can be extended further, so each is an essential prime implicant. The minimal sum-of-products expression is therefore AB + BC + CD.