Logic gates

Two conditions for one output

Imagine two signals: A means “permission” and B means “button pressed.” With AND, Y is 1 only when both are 1. If either is 0, the output is 0. The truth table lists all four possibilities, including those you are not currently testing.

Switch to XOR: with A = 1 and B = 1, the output becomes 0. XOR means the inputs differ, not just that one or more are active. This distinction is useful in digital comparators and adders.

Seven operations, one convention

• AND (&): all inputs must be 1.
• OR (≥1): at least one input must be 1.
• NOT (1 with inversion bubble): inverts its single input.
• NAND: inverts the AND output.
• NOR: inverts the OR output.
• XOR (=1): exactly one of the two inputs is 1.
• XNOR: inverts XOR; 1 when the inputs match.

We use rectangular IEC-style symbols. The small output circle means inversion, not a connection. An arrow marks the active truth-table row as well as background color. Each button announces its state through both text and its accessible state.

A bit is not a universal voltage

0 and 1 are ideal logic states, not necessarily 0 V and 5 V. Thresholds depend on the logic family and supply voltage. This tool does not model floating inputs, propagation delays, contact bounce or undefined states.

NOT uses only A and has two rows. The other six gates use exactly two inputs and four rows. XOR means “exactly one” in this two-input case.

Common mistakes

• Confusing OR with XOR when both inputs are on.
• Applying the inversion bubble to one input when the diagram places it at the output.
• Assuming a disconnected input is automatically 0 in a real circuit.

Try it yourself