Logic Gates and Circuits

The opposite direction is also examined: you are given a Boolean expression and have to draw the circuit.

Method. (1) Read the expression inside out: innermost brackets first, then NOT, then AND, then OR. (2) Use one gate per operator. (3) Wire each gate's inputs to the correct preceding signal (a labelled input variable, or the output of an earlier gate). (4) Make sure NOT gates appear before the negated value enters its next gate. (5) Label the last gate's output Q (or whatever name the question uses).

Example — draw the circuit for Q = (A AND B) OR (NOT C).

Walking through the expression:

1. The innermost terms are A AND B and NOT C. So you need an AND gate with inputs A and B, and a NOT gate with input C.
2. These two intermediate signals feed an OR gate to make the final output.

The circuit therefore has three gates: an AND, a NOT, and an OR. The OR gate's output is labelled Q. The AND gate sits at the top, the NOT gate at the bottom, and both feed the OR gate on the right.

Example — draw the circuit for P = ((NOT A) OR B) NAND C.

1. Start with NOT A: one NOT gate with input A.
2. Then (NOT A) OR B: one OR gate with inputs from the NOT gate and the input B.
3. Then … NAND C: one NAND gate with inputs from the OR gate and the input C.
4. The NAND gate's output is labelled P.

The whole circuit has four gates wired in series (NOT → OR → NAND), with C joining at the last gate.

Example — turning a written specification into a circuit.

"A burglar alarm sounds (output S = 1) when the building is armed (input A) and at least one of the door sensor (input B) or window sensor (input C) is triggered."

Translate the words: "at least one of B or C" is B OR C; "and" combines this with A. So S = A AND (B OR C).

To draw it: an OR gate on B and C, then an AND gate whose inputs are A and the OR gate's output. The AND gate's output is S.