How to use the Truth Table Generator
- 1. Type the expressionUse A·B, A+B, A' or words like AND, OR, NOT, XOR.
- 2. GenerateThe tool finds the variables and works out every combination.
- 3. Use the resultRead the table, copy the minterms or download it as CSV.
Symbols the generator understands
- AND:
·*&AND, or two letters side by side (AB). - OR:
+|OR - NOT:
'after a letter (A'), or!~NOTbefore it. - XOR:
^⊕XOR; alsoNAND,NOR,XNOR. - Implies:
->; if and only if:<->.
Precedence from highest to lowest: NOT, AND, XOR, OR, implies, iff. Use brackets whenever you are unsure. With n variables the table has 2ⁿ rows, so 3 variables give 8 rows and 8 variables give 256.
Worked example
For A·B + A'·C (a 2-to-1 multiplexer: output B when A is 1, else C), the variables are A, B and C, so there are 8 rows. The output is 1 in rows 001, 011, 110 and 111, so the tool shows 4 of 8 rows and minterms Σm(1, 3, 6, 7).
The canonical SOP lists one product per 1 row: A'B'C + A'BC + ABC' + ABC. The canonical POS lists one sum per 0 row. These forms are correct but long. To simplify, put the minterms 1, 3, 6, 7 into the K-map solver, which gives back A'C + AB.
The generator also tells you if the expression is a tautology (always 1, such as A + A'), a contradiction (always 0, such as A·A') or neither. That is handy for checking logic laws in discrete maths.
Frequently asked questions
Why is AB read as A AND B?
In digital electronics, writing letters next to each other means AND. Variables are single letters, so AB is two variables.
How are rows ordered?
In binary counting order with the first variable alphabetically as the most significant bit, starting from all zeros.
Can I use 0 and 1 in the expression?
Yes. 1 is true and 0 is false, so A + 1 is always 1.
Is the truth table generator free?
Yes, it is free. Type as many expressions as you like; we ask for your name and WhatsApp number once when you generate your first table, never again on our tools.