Tools

Boolean Expression Simplifier

Build a truth table and Karnaugh map for any expression over variables A–D. Supports AND (&&), OR (||), NOT (!), XOR (^), NAND, NOR and XNOR, and derives the canonical Sum of Products.

Try

Operators&& AND|| OR! NOT^ XORNAND NANDNOR NORXNOR XNOR

Classification

Contingent

depends on the inputs

Variables

A, B, C

8 combinations

True rows

4 / 8

50% of inputs

Minterms

3, 5, 6, 7

rows where output is 1

Truth tablerows where the output is 1 are highlighted

#	A	B	C	Output
0	0	0	0	0
1	0	0	1	0
2	0	1	0	0
3	0	1	1	1
4	1	0	0	0
5	1	0	1	1
6	1	1	0	1
7	1	1	1	1

Karnaugh mapGray-coded — adjacent cells differ by one variable

A \ BC	00	01	11	10
0	0m0	0m1	1m3	0m2
1	0m4	1m5	1m7	1m6

Neighbouring 1s (including across the edges) form groups that collapse into a simpler term.

Canonical Sum of Productsone AND term per row where the output is 1

(!A && B && C) || (A && !B && C) || (A && B && !C) || (A && B && C)