🔗 Paper 1 · Topic 2: Boolean Logic
2.3a Boolean Logic: Logic Gates
Edexcel 1CP2 · GCSE Computer Science · ~14 min read · ✅ Free
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Boolean Logic

Computers process data using binary (0 and 1). Boolean logic applies mathematical rules to these binary values. Everything a computer does — from simple arithmetic to complex decisions — is built from logic gates.

  • Boolean values: TRUE (1) or FALSE (0)
  • Boolean operators: AND, OR, NOT, XOR, NAND, NOR

NOT Gate (Inverter)

⊘

NOT — Inverts the input

Symbol: NOT A or Ā
Output is the opposite of the input.

ANOT A
01
10

AND Gate

⋂

AND — Both inputs must be 1

Symbol: A AND B or A · B
Output is 1 only when ALL inputs are 1.

ABA AND B
000
010
100
111

OR Gate

⋃

OR — At least one input must be 1

Symbol: A OR B or A + B
Output is 1 when ANY input is 1.

ABA OR B
000
011
101
111

XOR Gate (Exclusive OR)

⊕

XOR — Exactly one input must be 1

Symbol: A XOR B or A ⊕ B
Output is 1 when inputs are different. Output is 0 when both are the same.

ABA XOR B
000
011
101
110

NAND & NOR Gates

NAND = NOT AND (inverted AND output). NOR = NOT OR (inverted OR output).

ABNANDNOR
0011
0110
1010
1100

NAND is a universal gate — any other gate can be built entirely from NAND gates.

Logic Gate Symbols (British Standard)

For the exam, know these shape descriptions:

  • NOT — triangle with a bubble at output
  • AND — D-shaped (flat input side, curved output)
  • OR — curved on both sides (like a shield)
  • NAND — AND shape with a bubble at output
  • NOR — OR shape with a bubble at output
  • XOR — OR shape with an extra curved line at inputs
Exam tip: Edexcel 1CP2 expects you to complete truth tables for NOT, AND, OR, XOR, NAND, NOR — and combinations of gates. Practice these systematically. XOR is 1 when inputs DIFFER, 0 when they are the SAME.
⚠️ Common Mistakes
  • Confusing XOR and OR: OR is 1 when both inputs are 1; XOR is 0 when both are 1
  • Forgetting NAND = inverted AND, NOR = inverted OR
  • Mislabelling gate shapes in diagrams
  • Not working through gate combinations column by column in truth tables
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Worksheet — 2.3a Boolean Logic: Logic Gates

8 Edexcel-style questions · instantly marked

Q1State the output of an AND gate when inputs A=1 and B=0.[1]
✅ Mark scheme
Output = 0 [1]. An AND gate only outputs 1 when BOTH inputs are 1.
Q2Complete the truth table for a NOT gate. Input A: 0, 1. Give both outputs.[2]
✅ Mark scheme
NOT 0 = 1 [1]; NOT 1 = 0 [1].
Q3What is the difference between an OR gate and an XOR gate?[2]
✅ Mark scheme
OR outputs 1 when at least one input is 1, including when both are 1 [1]; XOR outputs 1 only when the inputs are different (exactly one is 1), outputting 0 when both are 1 [1].
Q4Give the output of a NAND gate for: A=1, B=1.[1]
✅ Mark scheme
Output = 0 [1]. NAND = NOT AND. AND(1,1)=1, so NOT 1 = 0.
Q5State when a NOR gate outputs 1.[1]
✅ Mark scheme
A NOR gate outputs 1 only when ALL inputs are 0 [1].
Q6What is a "universal gate" and which gate is considered universal?[2]
✅ Mark scheme
A universal gate is one from which any other logic gate can be built [1]; the NAND gate (and NOR gate) is considered universal [1].
Q7Complete all four rows of an XOR truth table (two inputs A and B).[4]
✅ Mark scheme
A=0,B=0 → 0 [1]; A=0,B=1 → 1 [1]; A=1,B=0 → 1 [1]; A=1,B=1 → 0 [1].
Q8A circuit has inputs A and B. The output is: (A AND B) then NOT applied to the result. What is the output when A=1, B=1?[2]
✅ Mark scheme
AND(1,1)=1 [1]; NOT(1)=0, so final output = 0 [1]. This is the NAND gate.
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Mini Test — Logic Gates

Timed exam-style test.

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