Truth Table for NAND

What NAND means

A NAND statement is the negation of AND. For two inputs, the output is false only when both inputs are true. In every other case, the output is true.

How to build the truth table

1. List all input combinations in the usual order: TT, TF, FT, FF.
2. Find the AND result for each row.
3. Negate that result to get NAND.
4. Fill in the output column carefully.

For two variables, the pattern is:

• T NAND T = F
• T NAND F = T
• F NAND T = T
• F NAND F = T

Simplifying the final answer

If the exercise asks for a simplified form, remember that NAND is the complement of AND. So the expression is true whenever the AND part is false. You can often check your final result by asking: “Is there any row where both inputs are true?” If yes, that is the only row where NAND becomes false.

Quick check

After completing the table, verify that:

• there is exactly one false output for two-input NAND,
• that false output occurs only in the row where both inputs are true.

If your table matches that pattern, the answer is correct.