Skip to main content

K-map: 4-variable minterm list

Short answer

K-map grouping: quad (m1,m3,m9,m11) gives B'D; quad (m3,m7,m11,m15) gives CD; pair (m14,m15) gives ABC. Simplified expression: F = B'D + CD + ABC.

Simplify an expression F(A,B,C,D) = Σ(1,3,7,9,11,14,15) by using K-map.

F(A,B,C,D) = Σm(1, 3, 7, 9, 11, 14, 15).

K-map

           CD
         00  01  11  10
 AB=00 | 0 | 1 | 1 | 0 |
 AB=01 | 0 | 0 | 1 | 0 |
 AB=11 | 0 | 0 | 1 | 1 |
 AB=10 | 0 | 1 | 1 | 0 |

Groups

  1. Quad (m1, m3, m9, m11): B = 0, D = 1 gives B'D.
  2. Quad (m3, m7, m11, m15): C = 1, D = 1 gives CD.
  3. Pair (m14, m15): A = 1, B = 1, C = 1 gives ABC.

All 7 minterms are covered, and each group is needed (m1, m9 only in group 1; m7 only in group 2; m14 only in group 3).

Answer: F = B'D + CD + ABC

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Basic Electronics Engineering chapter 6 questions →