Boolean Algebra Calculator

Use ' or ! or ~ for NOT, + or OR for OR, . or * or juxtaposition for AND, and XOR / NAND / NOR / -> / <-> for the rest.
Left-most variable is the most significant bit of the minterm number. Defaults to alphabetical order.
Simplified (sum of products)
A + B
Boolean Algebra Calculator
Simplified (product of sums)
(A + B)
Canonical sum of products
A'B + AB' + AB
Canonical product of sums
(A + B)
Terms in the minimal SOP
2
Literals in the minimal SOP
2
Classification
contingent (true for some inputs)
Expression as parsed
A OR A' AND B
Worked out from M. Morris Mano and Michael D. Ciletti, Digital Design, Chapter 2 (Boolean Algebra and Logic Gates) and Chapter 3 (Gate-Level Minimization) and 1 other source.

How this is worked out

6 steps
  1. Variables in order: A, B (2 variables, 4 rows).
  2. Rows where the expression is 1 (minterms): 1, 2, 3.
  3. Canonical sum of products: A'B + AB' + AB
  4. Quine-McCluskey prime implicants: B, A
  5. Minimum cover: A + B (2 term(s), 2 literal(s)).
  6. Complement minimised and De Morgan applied gives the product of sums: (A + B)
Mintermstable
1, 2, 3
Maxtermstable
0
Variablestable
A, B
Prime implicantstable
B, A
Truth tabletable
ABF
000
011
101
111

Results are general information, not financial, tax, legal, medical or engineering advice.