← IGCSE Computer Science Paper 2

The NOR gate

The NOR gate: output X is 1 only when both inputs A and B are 0. It is OR followed by NOT, so the truth table output is 1 0 0 0. Its symbol is OR with a small circle.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 12

Understanding The NOR gate in IGCSE Computer Science Paper 2

What it does: The brackets make OR happen first, then NOT inverts that result. This is the same as A NOR B. Only row 00 gives 1. The three rows with at least one 1 input give 0, so the column reads 1 0 0 0. NOR is the opposite of OR. It outputs 1 only when both inputs are 0. 0 1 1 1 is the OR column. NOR is OR with every output flipped, so it is 1 0 0 0. A small circle on the output means NOT. OR plus the circle is NOR. AND plus the circle is NAND.

Common mistakes: A NOR gate outputs 1 only when both inputs are 0. When A is 0 and B is 1, the output must be 0, so the line should be 0 1 | 0. NOR is OR followed by NOT. NOT (A AND B) is the NAND gate. The line should be X = NOT (A OR B).

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This module's key terms are also in a printable crossword (Modules 539–551) and word search (Modules 539–580).

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Learning
Duo
A NOR gate has two inputs, A and B. When is the output X equal to 1?
When A = 1 or B = 1Only when A = 0 and B = 0
Matches
X = NOT (A AND B)
↓
This is NAND, not NOR. NOR needs OR inside the brackets: X = NOT (A OR B).
Applying
Meanings
Term
X = NOT (A OR B)
Meaning
The NOR gate: output X is 1 only when both inputs A and B are 0. It is OR followed by NOT, so the truth table output is 1 0 0 0. Its symbol is OR with a small circle.
Practice
X = A NOR B
Testing
Gaps
X = NOT (A B)
Check Answer
Spots
20 0 | 1
30 1 | 1

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Quick Questions

1. A NOR gate has two inputs, A and B. When is the output X equal to 1?
A. Only when A = 0 and B = 0 ✓
B. When A = 1 or B = 1
NOR is the opposite of OR. It outputs 1 only when both inputs are 0.
2. Which output column (for A,B = 00, 01, 10, 11) is correct for a NOR gate?
A. 0 1 1 1
B. 1 0 0 0 ✓
0 1 1 1 is the OR column. NOR is OR with every output flipped, so it is 1 0 0 0.
3. Which symbol shows a NOR gate?
A. The AND symbol with a small circle on the output
B. The OR symbol with a small circle on the output ✓
A small circle on the output means NOT. OR plus the circle is NOR. AND plus the circle is NAND.
4. Which expression describes a NOR gate?
A. X = NOT (A OR B) ✓
B. X = (NOT A) OR B
NOT must apply to the whole of (A OR B), so the brackets matter. (NOT A) OR B is a different expression.
5. A NOR gate has inputs A = 1 and B = 0. What is the output X?
A. 0 ✓
B. 1
A OR B = 1, and NOT 1 = 0. So X = 0.

Match the Pairs

X = A NOR B → The NOR gate: two inputs A and B, one output X, which is the opposite of OR
A = 0, B = 0, X = 1 → The only row where a NOR gate outputs 1: both inputs are 0
NOR is OR followed by NOT, so the result of the OR is flipped → X = NOT (A OR B)
The NOR output column for input rows 00, 01, 10 and 11, in that order → 1 0 0 0
X = NOT (A AND B) → This is NAND, not NOR. NOR needs OR inside the brackets: X = NOT (A OR B).
A = 1, B = 0, X = 1 → A NOR gate outputs 0 when any input is 1. With A = 1 and B = 0, X should be 0.

Key Term

X = NOT (A OR B)
The NOR gate: output X is 1 only when both inputs A and B are 0. It is OR followed by NOT, so the truth table output is 1 0 0 0. Its symbol is OR with a small circle.

Fill in the Blanks

1. X = NOT (A OR B)
Hint: Type the gate name inside the brackets that NOR is the opposite of.
2. X = NOT (A OR B)
Hint: Type the operator that flips the result of the whole bracket.
3. X = A NOR B
Hint: Type the gate name written between A and B in the short expression.
4. When A = 0 and B = 0, X = 1
Hint: Type the single output value NOR gives when both inputs are off.
5. Symbol: OR with a small circle on output
Hint: Type the name of the small shape added at the output to show the NOT.

Spot the Error

Question 1
A A B | X
B 0 0 | 1
C 0 1 | 1
D 1 0 | 0
E 1 1 | 0
Line C — A NOR gate outputs 1 only when both inputs are 0. When A is 0 and B is 1, the output must be 0, so the line should be 0 1 | 0.
Question 2
A A = 0
B B = 0
C X = NOT (A AND B)
D OUTPUT X
Line C — NOR is OR followed by NOT. NOT (A AND B) is the NAND gate. The line should be X = NOT (A OR B).
Question 3
A NOR is AND followed by NOT
B X = NOT (A OR B)
C A = 1, B = 0
D X is 0
Line A — NOR is OR followed by NOT. AND followed by NOT would be NAND. The line should say NOR is OR followed by NOT.
Question 4
A A B | X (NOR gate)
B 1 1 | 1
C 1 0 | 0
D 0 0 | 1
Line B — A NOR gate gives 0 whenever at least one input is 1. With A = 1 and B = 1 the output is 0, so the line should be 1 1 | 0.
Question 5
A X = NOT A OR B
B A = 0
C B = 1
D OUTPUT X
Line A — Without brackets, NOT applies only to A. NOR needs NOT to apply to the whole OR result, so the line should be X = NOT (A OR B).

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