Corner group

Also called: four corners, four-corner group, K-map corners, corner cells

The group made of the four corner cells of a 4-variable K-map, m0, m2, m8 and m10. Thanks to wrap-around they are mutually adjacent and read as B'D'.

On a 4-variable K-map, the four corner cells m0, m2, m8 and m10 form a single group of 4.

Why they belong together: the map wraps left to right and top to bottom.

m0 and m2 are the two ends of the top row: adjacent.
m8 and m10 are the two ends of the bottom row: adjacent.
m0 and m8 are the two ends of the left column: adjacent.
m2 and m10 are the two ends of the right column: adjacent.

So the four corners make a 2×2 square that happens to be split across both seams. Their codes are 0000, 0010, 1000 and 1010. A and C change; B and D stay 0. The term is .

On a 3-variable map the same idea gives the four cells of the two end columns, m0, m2, m4, m6, which read as .

Corner groups are easy to miss because the cells look as far apart as possible. Make a habit of checking all four corners whenever any one of them holds a 1.

AB\CD	00	01	11	10
00	1m0	0m1	0m3	1m2
01	0m4	0m5	0m7	0m6
11	0m12	0m13	0m15	0m14
10	1m8	0m9	0m11	1m10

Worked example

Example

Corners plus a pair

Simplify F = Σm(0, 2, 8, 10, 14).

AB\CD	00	01	11	10
00	1m0	0m1	0m3	1m2
01	0m4	0m5	0m7	0m6
11	0m12	0m13	0m15	1m14
10	1m8	0m9	0m11	1m10

1.
The four corners are all 1: group them → .
2.
m14 (1110) is left. Its neighbors are m6, m10, m12 and m15. Only m10 is a 1.
3.
Pair m10 and m14: A = 1, C = 1, D = 0 stay fixed; B changes → .
4.
F = .

Common mistakes

Pairing two diagonal corners, such as m0 and m10. They differ in two bits; only all four together form a group.
Covering the corners with two pairs, which costs an extra term and an extra literal each.
Thinking the cells between the corners must also be 1s. The four corners alone make the group.

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Corner group is taught in Karnaugh Maps.

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