Boolean logic: AND, OR, NOT gates and truth tables

Boolean logic is tested on every OCR J277 Paper 2. Expect truth table questions (completing a table for a given circuit), circuit diagram questions (draw the gates for a Boolean expression), and expression questions (write the expression for a circuit). These are reliable marks — learn the rules.

Basic logic gates

NOT gate (inverter)

A	NOT A
0	1
1	0

• Inverts the input. If A is true (1), NOT A is false (0). Written: ¬A or NOT A or A'.

AND gate

A	B	A AND B
0	0	0
0	1	0
1	0	0
1	1	1

• Output is 1 only if both inputs are 1. Written: A AND B or A · B.

OR gate

A	B	A OR B
0	0	0
0	1	1
1	0	1
1	1	1

• Output is 1 if at least one input is 1. Written: A OR B or A + B.

Combined gates — worked example

Expression: NOT (A AND B) OR C

Step 1: Evaluate A AND B. Step 2: Apply NOT to that result. Step 3: OR the result with C.

Full truth table (A, B, C all possible combinations — 8 rows for 3 inputs: 2³):

A	B	C	A AND B	NOT(A AND B)	NOT(A AND B) OR C
0	0	0	0	1	1
0	0	1	0	1	1
0	1	0	0	1	1
0	1	1	0	1	1
1	0	0	0	1	1
1	0	1	0	1	1
1	1	0	1	0	0
1	1	1	1	0	1

Drawing logic circuits

• NOT: triangle with a small circle at the output.
• AND: flat-backed D-shape gate.
• OR: curved D-shape gate (input side concave).

Wires connect inputs → gates → output.

Common OCR exam mistakes

1. AND gate confusion: "both inputs must be 1" — even 1+0 gives 0. Only 1 AND 1 = 1.
2. NOT applied after the gate (NAND-like result) — read expressions carefully for brackets: NOT(A AND B) ≠ NOT A AND NOT B.
3. Row count for truth tables: 2 inputs → 4 rows (2²); 3 inputs → 8 rows (2³). Always list binary in order (000, 001, 010, 011, …).
4. Writing the wrong number of columns — include intermediate columns for each gate in the expression.