beginner Digital Electronics

Logic Gates & Boolean Algebra

Explore logic gates using interactive truth tables. Understand AND, OR, NOT, XOR, NAND, NOR, and XNOR with SOP forms.

Boolean Expression

Operators: AND OR NOT XOR NAND NOR XNOR — e.g. (A AND B) OR NOT C

Sum of Products (SOP)

NOT A AND NOT B AND NOT C
  OR  NOT A AND B AND NOT C
  OR  A AND NOT B AND NOT C
  OR  A AND B AND NOT C
  OR  A AND B AND C

The truth table generator evaluates any Boolean expression. The default expression is 'A AND B OR NOT C'. Try it — you should see 8 rows (2³ combinations).

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Type any expression using variables A–Z and operators: AND OR NOT XOR NAND NOR XNOR. Parentheses are supported.
Change the expression to just 'A AND B'. The table has 4 rows. Only the last row (A=1, B=1) gives output 1. This is the AND gate behaviour.

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AND: output is 1 only when ALL inputs are 1. Used for enabling a signal (both conditions must be true).
Try 'A OR B'. Now output is 1 when ANY input is 1. Only A=0, B=0 gives output 0.

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OR: output is 1 when AT LEAST ONE input is 1. Used for combining independent conditions.
Try 'NOT A'. Only one variable, two rows. NOT inverts the signal: 0 becomes 1, 1 becomes 0.

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NOT (inverter) is the simplest gate. It is the fundamental building block — NAND and NOR gates are NOT-AND and NOT-OR.
Try 'A XOR B'. XOR (exclusive-OR) is 1 when inputs are DIFFERENT. XOR is used in parity checkers, adders, and cryptography.

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XOR is also called 'odd parity' — it's 1 when an odd number of inputs are 1.
Try a more complex expression: '(A AND B) OR (NOT A AND C)'. Expand the Sum of Products section at the bottom to see the canonical SOP form.

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SOP (Sum of Products) is a standard canonical form — each minterm (row where output = 1) becomes an AND term; all terms are OR'd together.