Isolated 1

Also called: isolated minterm, single-cell group, lone 1, isolated cell, isolated one

A 1 on a K-map with no adjacent 1s or don't-cares, even across the wrap. It forms a group of one cell, whose term is the full minterm.

Sometimes a 1 has no neighboring 1 at all. Check every cell next to it, including across the wrap, and if none holds a 1 or an X, the cell is isolated.

An isolated 1 still has to be covered, so it becomes a group of one cell. A group of 2⁰ = 1 cell removes no variables, so its term is the complete minterm, with every variable present.

That's legal, and you must not skip it. A single-cell group is also automatically an essential prime implicant: it can't grow, and nothing else covers that 1.

An isolated 1 is the most expensive kind of term, so it's worth checking carefully before you accept one. Look again at:

the cell at the other end of its row and of its column
any don't-cares next to it, which could be used to pair it up

Functions like the odd function have every 1 isolated: their 1s form a checkerboard, and the minimal SOP is just the list of minterms.

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

Worked example

Example

One pair and one isolated 1

Simplify F = Σm(0, 1, 10), shown above.

1.
m0 and m1 sit side by side in the top row → .
2.
m10 = 1010. Its neighbors are m2, m8, m11 and m14. All are 0.
3.
So m10 is isolated. Its term is the full minterm .
4.
F = .

Common mistakes

Leaving an isolated 1 uncovered because it doesn't fit any group.
Forcing it into a diagonal group with a nearby 1.
Declaring a 1 isolated without checking the wrap-around neighbors and nearby don't-cares.

Practice Isolated 1

Interactive questions with instant feedback and a worked solution for every wrong answer.

Practice exams

Karnaugh Maps: Exam 4 · 1 question

Learn it step by step

Isolated 1 is taught in Karnaugh Maps.

Karnaugh Maps →

All terms