F(A,B,C,D) = Σm(4,5,6,7,8,9,10,11) — Karnaugh map
coretwo octets, 2 terms
Answer
A′ · B + A · B′
Why this example is worth doing
Two blocks of eight that each reduce to a two-literal term, and a good demonstration that groups may overlap in principle but need not. The interesting property is that the function is A ⊕ B — the expression Ā·B + A·B̄ is exactly the XOR of the two most significant variables, and C and D are irrelevant. The converter bar therefore offers a one-gate diagram for a function whose map has eight 1s in it, which is the clearest argument on the site for looking at more than one representation.
Try your own input in the Karnaugh map solver. Group a 2- to 6-variable map yourself and have every group marked right or wrong.
How the answer is reached
Quine–McCluskey
| # | Term |
|---|---|
| 1 | A′ · B |
| 2 | A · B′ |
| # | Cover |
|---|---|
| 1 | A′ · B + A · B′ |
Warning:
2 term(s), 4 literal(s); 2 essential prime implicant(s).
Truth table
| # | A | B | C | D | F |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 2 | 0 | 0 | 1 | 0 | 0 |
| 3 | 0 | 0 | 1 | 1 | 0 |
| 4 | 0 | 1 | 0 | 0 | 1 |
| 5 | 0 | 1 | 0 | 1 | 1 |
| 6 | 0 | 1 | 1 | 0 | 1 |
| 7 | 0 | 1 | 1 | 1 | 1 |
| 8 | 1 | 0 | 0 | 0 | 1 |
| 9 | 1 | 0 | 0 | 1 | 1 |
| 10 | 1 | 0 | 1 | 0 | 1 |
| 11 | 1 | 0 | 1 | 1 | 1 |
| 12 | 1 | 1 | 0 | 0 | 0 |
| 13 | 1 | 1 | 0 | 1 | 0 |
| 14 | 1 | 1 | 1 | 0 | 0 |
| 15 | 1 | 1 | 1 | 1 | 0 |