Karnaugh Mapping Calculator

Most significant first. The first half index the map rows, the rest the columns.
Cells that may be treated as 1 or 0, whichever gives the simpler cover.
One character per row in cell order: 1, 0, or x for a don't care.
Minimal sum of products
B'C' + B'D' + A'C'D
Karnaugh Map Solver
Minimal product of sums
(A' + B')(B' + D)(C' + D')
Terms (AND gates)
3
Literals (gate inputs)
7
Row variables
AB
Column variables
CD
Canonical sum of products
A'B'C'D' + A'B'C'D + A'B'CD' + A'BC'D + AB'C'D' + AB'C'D + AB'CD'
Worked out from M. Karnaugh, "The Map Method for Synthesis of Combinational Logic Circuits", Transactions of the AIEE 72 (1953), 593-599 and 1 other source.

How this is worked out

6 steps
  1. Map over A, B, C, D: 4 rows (AB) by 4 columns (CD), Gray-coded so neighbours differ in one variable.
  2. 1-cells: 0, 1, 2, 5, 8, 9, 10.
  3. Prime implicants (all maximal groups): B'C', B'D', A'C'D
  4. Essential prime implicants (each is the only group covering some 1): B'C', B'D', A'C'D
  5. Minimum cover: F = B'C' + B'D' + A'C'D (3 term(s), 7 literal(s)).
  6. Minimising the 0-cells and applying De Morgan gives F = (A' + B')(B' + D)(C' + D').
Prime implicantstable
B'C', B'D', A'C'D
Essential prime implicantstable
B'C', B'D', A'C'D
Groups in the chosen covertable
termcellssize
B'C'0, 1, 8, 94
B'D'0, 2, 8, 104
A'C'D1, 52
Karnaugh maptable
1011AB0001
100011
000101
001100
101011
Row labels (Gray code)table
00, 01, 11, 10
Column labels (Gray code)table
00, 01, 11, 10
Minterms usedtable
0, 1, 2, 5, 8, 9, 10

Results are general information, not financial, tax, legal, medical or engineering advice.