Grouping rules
- Groups contain 1, 2, 4, 8, or another power-of-two number of cells.
- Make groups as large as possible and cover every required 1.
- Groups may overlap, and map edges wrap around.
- Use don't-cares only when they make a useful larger group.
1010111110101111
Opposite edges are adjacent. Visual grouping should follow Gray-code row and column labels.
Worked example
F(A,B,C,D) = Σm(0,2,5,7,8,10,13,15)
The minterms form two groups of four. In the first group B = 0 and D = 0, giving B'D'. In the second group B = 1 and D = 1, giving BD.
Simplified result: F = B'D' + BD, which is B XNOR D. A and C disappear because they change within each group.
SOP and POS
Group 1s to derive sum-of-products. Group 0s to derive product-of-sums. Choose the form that matches the required implementation and gives simpler logic.
Common mistakes
- Ordering rows or columns as binary 00, 01, 10, 11 instead of Gray code 00, 01, 11, 10.
- Making diagonal groups or non-power-of-two groups.
- Missing wrap-around adjacency between opposite edges.
- Using every don't-care even when it does not simplify the expression.