Connect the gates and watch the lamp light up.

Circuit editor

AND, OR, NOT, XOR, NAND, NOR, XNOR and BUF gates on a grid (2–4 inputs for multi-input gates), switch, lamp and clock (0.5–8 Hz). Place a part by tapping it and choosing its spot, or by dragging; connect wires by dragging between pins, tapping them in turn or with the "Connect…" dialog.

Live simulation

Event-driven, with a one-step delay for every gate. Circuits with feedback (SR latch) settle into a state; a circuit that does not settle is shown as "oscillating". Wires carrying 1 glow.

Truth table and expression

The table is built automatically from the switches and lamps (up to 8 inputs), with the current row highlighted. The Boolean expression is written as a sum of products simplified with Quine–McCluskey for up to 4 inputs, and XOR forms are recognised. "Copy table" gives tab-separated text.

12 exercises

NOT, gates, half and full adder, NAND only, SR latch, multiplexer, decoder, comparator, 2-bit adder, D latch, majority vote. "Test" tries every input combination and shows the first wrong row; progress is saved.

Build circuit from table

Fill in a truth table or type an expression (A·B + ¬C, A ⊕ B …); Boolia builds the circuit in simplified form, with up to 4 inputs and 4 outputs.

Run step by step

Each step is one gate delay; the parts to be computed in the next step are marked. The clock can also be ticked by hand.

All features