K-map Structure
CD
AB
00
01
11
10
00
m0
m1
m3
m2
01
m4
m5
m7
m6
11
m12
m13
m15
m14
10
m8
m9
m11
m10
Gray Code Order: 00 → 01 → 11 → 10
Only one bit changes between adjacent cells.
Minterm Formula:
mn = 8A + 4B + 2C + D
Example: AB=01, CD=11 → m7
Variable Regions:
A=1: bottom two rows
B=1: middle two rows
C=1: middle two columns
D=1: columns 01 and 11
Adjacency Property: Adjacent cells (including wrap-around) differ by exactly one variable, enabling grouping for simplification.
Interactive K-map (Click cells to toggle: 0 → 1 → X → 0)
CD
AB
↑ wraps to bottom
↓ wraps to top
← wraps
wraps →
CD/AB
00
C'D'
01
C'D
11
CD
10
CD'
00
A'B'
m00
m10
m30
m20
01
A'B
m40
m50
m70
m60
11
AB
m120
m130
m150
m140
10
AB'
m80
m90
m110
m100
0
False
1
True
X
Don't Care
Product Term Entry

Or select minterms directly:

Teaching Notes

Toroidal Adjacency: The K-map wraps both horizontally and vertically. Top row is adjacent to bottom row; left column is adjacent to right column.
Valid Group Sizes: Groups must contain 2n cells: 1, 2, 4, 8, or 16 cells.
Corner Group: The four corners (m0, m2, m8, m10) form a valid group! They simplify to B'D'.
Try these examples:
A'B'C'D' AB B'D' 2 terms