Logic Gates and Circuits

When the question gives you a circuit and a specific set of input values (for example A = 1, B = 0, C = 1), the safest method is to process the gates from left to right, in the order the signals flow.

Method. (1) Mark each input on the diagram with its 0 or 1. (2) For each gate, look only at the values arriving at its inputs and apply the gate's rule to get its output. (3) Pass that output forward as one of the inputs to the next gate. (4) Repeat until you reach the final output Q.

Always write down the intermediate value at the output of every gate, even if you can do the calculation in your head. Examiners award method marks for the intermediates, so if your final Q is wrong, you still pick up marks for the steps.

Example — work out Q for the circuit Q = (A OR B) AND (NOT C) when A = 0, B = 1, C = 0.

• Gate 1 (OR with inputs A, B): 0 OR 1 = 1. Call this P1 = 1.
• Gate 2 (NOT with input C): NOT 0 = 1. Call this P2 = 1.
• Gate 3 (AND with inputs P1, P2): 1 AND 1 = 1. So Q = 1.

If A = 1, B = 1, C = 1 instead, the same circuit gives P1 = 1, P2 = 0, and Q = 1 AND 0 = 0.

Two sanity checks you can use on any row:

• An AND gate with any 0 input has output 0.
• An OR gate with any 1 input has output 1.

If your intermediate value disagrees with either of those, you have made a slip.