Logic gates

What you need to know

• ✓NOT gate (inverter): Has 1 input and 1 output. Inverts the input: an input of 0 gives 1; an input of 1 gives 0.
• ✓AND gate: Has 2 inputs. The output is 1 only if BOTH input A AND input B are 1.
• ✓OR gate: Has 2 inputs. The output is 1 if AT LEAST ONE input (A OR B or both) is 1.
• ✓XOR (exclusive OR) gate: Has 2 inputs. The output is 1 if EXACTLY ONE input is 1, but 0 if both inputs are 1 or both are 0.
• ✓Truth tables list every possible combination of inputs and the resulting output for a logic gate or circuit.
• ✓A circuit with n inputs has 2ⁿ possible input combinations (2 inputs = 4 rows, 3 inputs = 8 rows).

What you don’t need

• NAND and NOR gates — the AQA specification explicitly states students do not need to know or use NAND and NOR gates.
• Karnaugh maps and De Morgan's Laws — these are A-Level Computer Science topics.
• Circuits with more than 3 inputs.

Worked examples

1. Draw the truth table for an XOR gate with inputs A and B and output Q.

   1. Row 1: A = 0, B = 0 -> Q = 0 (neither is 1).
   2. Row 2: A = 0, B = 1 -> Q = 1 (exactly one is 1).
   3. Row 3: A = 1, B = 0 -> Q = 1 (exactly one is 1).
   4. Row 4: A = 1, B = 1 -> Q = 0 (both are 1, so XOR outputs 0).

   Answer: A=0, B=0 -> 0; A=0, B=1 -> 1; A=1, B=0 -> 1; A=1, B=1 -> 0.

2. A security alarm circuit has two sensors: Motion (M) and Window (W), plus an Arm switch (A). The alarm sounds (Q=1) if the system is Armed AND (either Motion is detected OR the Window is opened). Write the output when A=1, M=0, and W=1.

   1. Evaluate the OR branch: M OR W = 0 OR 1 = 1.
   2. Evaluate the AND gate: A AND (result of OR) = 1 AND 1 = 1.

   Answer: Q = 1 (The alarm sounds).

Common mistakes

• ✕Confusing OR and XOR: In everyday English 'or' often means one or the other, but in computing standard OR includes both inputs being 1. XOR requires strictly one input to be 1.
• ✕Drawing an AND gate symbol instead of an OR gate symbol: AND has a flat back and rounded front; OR has a curved back and pointed front.
• ✕Forgetting the inversion circle (bubble) on the tip of the NOT gate symbol.
• ✕Missing combinations in a 3-input truth table: Always count in binary sequence from 000 to 111 (000, 001, 010, 011, 100, 101, 110, 111) to avoid missing rows.