AS · Practice questions · Logic gates

Know your gates.

Six original Cambridge-style questions on logic gate symbols, functions and truth tables, with mark-scheme style solutions.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

One rule per gate.

AND needs both inputs 1; OR needs at least one; XOR needs them to be different.
NAND and NOR are AND and OR with every output inverted.
Symbols: flat back = AND family; curved back = OR family; extra curve = XOR; circle = inverted.
Rows: list inputs in binary counting order (00, 01, 10, 11) so none is missed.

Recall

[3 marks]

Define the function of each gate: (a) NAND, (b) NOR, (c) XOR.

(a) NAND: the output is 0 only when both inputs are 1; otherwise 1 (the inverse of AND). ✓
(b) NOR: the output is 1 only when both inputs are 0; otherwise 0 (the inverse of OR). ✓
(c) XOR: the output is 1 when the two inputs are different; 0 when they are the same. ✓

Apply

[4 marks]

Complete the truth table for X = A NOR B.

A	B	X
0	0
0	1
1	0
1	1

0, 0 gives 1. ✓
0, 1 gives 0. ✓
1, 0 gives 0. ✓
1, 1 gives 0. ✓

Recall

[3 marks]

Describe the standard symbol for each gate: (a) NOT, (b) NAND, (c) XOR.

(a) NOT: a triangle with a small circle at the output. ✓
(b) NAND: the AND shape (flat back, rounded front) with a small circle at the output. ✓
(c) XOR: the OR shape (curved back, pointed front) with an extra curved line behind the back. ✓

Analysis

[2 marks]

A two-input gate gives an output of 0 for exactly one combination of inputs, A = 1 and B = 1. Identify the gate and justify your answer.

NAND. ✓
AND outputs 1 only for 1, 1; NAND inverts every output, so it is 0 only for 1, 1. ✓

Explain

[2 marks]

Explain the difference between the functions of an OR gate and an XOR gate.

Both output 0 when both inputs are 0, and 1 when exactly one input is 1. ✓
When both inputs are 1, OR outputs 1 but XOR outputs 0. ✓

Apply

[2 marks]

Both inputs of a NOR gate are connected to the same signal P. Complete the outputs for P = 0 and P = 1, and state which gate the arrangement is equivalent to.

P = 0: 0 NOR 0 = 1; P = 1: 1 NOR 1 = 0. ✓
It is equivalent to a NOT gate. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.