Composing Gates: Predict the Chain

The fifth intro teaches the core skill of circuit design: predicting what a composite circuit does without running it. The walkthrough is below.

Predicting the chain

Two AND gates are chained: A and B feed the first, its output and C feed the second. The task: predict Q for A=1, B=1, C=0 without running the circuit. The correct answer is Q = 0: the first AND gives a one, but the second sees 1 and 0 on its inputs.

The rule: trace the signal

To predict a composite circuit, trace the signal from inputs to output, gate by gate. The output of the first gate becomes an input of the second. No one "pushes through" the chain: every gate honestly recomputes its inputs.

Transfer to any circuit

The trick works for a chain of any length and for gates of any type: walk left to right and write down the output of every element. Level 5 itself checks this skill with a truth table for a multi-gate circuit.

Where it is used

Composition is how circuits get built: complex ones are assembled from simple ones, like a house from bricks. An adder is made of gates, memory is made of gates, the processor in your phone is billions of gates chained together. There are only two moves: repeat a block and connect its output to the next input.