Skip to main content

K-map: 3-variable five-term expression

Short answer

F = Σ(0,1,3,4,7) groups: pair (m0,m1) yields x'y', (m0,m4) yields y'z', (m3,m7) yields yz. Simplified: F = x'y' + y'z' + yz.

Simplify the expression using k-map F(x,y,z) = xyz + x'y'z + xy'z' + x'y'z' + x'yz

F = xyz + x'y'z + xy'z' + x'y'z' + x'yz

Minterms: xyz = m7, x'y'z = m1, xy'z' = m4, x'y'z' = m0, x'yz = m3. F = Σm(0, 1, 3, 4, 7).

K-map

          yz
        00  01  11  10
 x = 0 | 1 | 1 | 1 | 0 |
 x = 1 | 1 | 0 | 1 | 0 |

Grouping

  1. Pair (m0, m1): x = 0, y = 0 gives x'y'.
  2. Pair (m0, m4): y = 0, z = 0 gives y'z' (the two cells of the 00 column).
  3. Pair (m3, m7): y = 1, z = 1 gives yz.

All five 1s are covered.

Answer: F = x'y' + y'z' + yz

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Basic Electronics Engineering chapter 6 questions →