← IGCSE Computer Science Paper 2

Where NOT applies in an expression

NOT before a bracket flips the whole bracket's result. In (NOT A) AND B, NOT flips only input A, so NOT (A AND B) gives different results.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 19

Understanding Where NOT applies in an expression in IGCSE Computer Science Paper 2

What it does: Only A is inverted. B goes into the AND gate unchanged, so the NOT is on one input only. The bracket holds A AND B, and NOT flips its output. This is the same as a NAND gate. NOT is placed before the bracket, so it flips the result of everything inside the bracket. A AND B = 1, and NOT makes it 0. For (NOT A) AND B: NOT 1 = 0, then 0 AND 1 = 0 as well, so check carefully. Here NOT (A AND B) is 0, and (NOT A) AND B is also 0, so use A = 0 and B = 1 to tell them apart.

Common mistakes: NOT must go before the bracket so it flips the whole result of A AND B. (NOT A) AND B only flips A, giving 0 here instead of 1. It should be X = NOT (A AND B). The comment says NOT applies to input A only, so A needs its own brackets: (NOT A) AND B. NOT (A AND B) flips the whole bracket and gives 1, not 0.

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This module's key terms are also in a printable crossword (Modules 552–561) and word search (Modules 539–580).

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Learning
Duo
In X = NOT (A AND B), what does NOT apply to?
The output of the bracket (A AND B)Only input A
Matches
X = NOT A AND B (meant: NOT (A AND B))
↓
The brackets are missing, so NOT applies only to A. The student wanted NOT to flip the whole result of A AND B.
Applying
Meanings
Term
NOT (A AND B)
Meaning
NOT before a bracket flips the whole bracket's result. In (NOT A) AND B, NOT flips only input A, so NOT (A AND B) gives different results.
Practice
X = NOT (A AND B)
Testing
Gaps
X = (A AND B)
Check Answer
Spots
1# A=1, B=0, so X must be 1
2X = (NOT A) AND B

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Quick Questions

1. In X = NOT (A AND B), what does NOT apply to?
A. The output of the bracket (A AND B) ✓
B. Only input A
NOT is placed before the bracket, so it flips the result of everything inside the bracket.
2. In X = (NOT A) AND B, what does NOT apply to?
A. Only input A ✓
B. The output of A AND B
The bracket contains only NOT A, so NOT flips input A before it reaches the AND gate. B is not changed.
3. A = 1 and B = 1. Which expression gives X = 0?
A. (NOT A) AND B
B. NOT (A AND B) ✓
A AND B = 1, and NOT makes it 0. For (NOT A) AND B: NOT 1 = 0, then 0 AND 1 = 0 as well, so check carefully. Here NOT (A AND B) is 0, and (NOT A) AND B is also 0, so use A = 0 and B = 1 to tell them apart.
4. A = 0 and B = 1. Which expression gives X = 1?
A. NOT (A AND B)
B. (NOT A) AND B ✓
(NOT A) AND B: NOT 0 = 1, then 1 AND 1 = 1. NOT (A AND B): 0 AND 1 = 0, then NOT 0 = 1. Both give 1, so try A = 1, B = 0 to separate them.
5. A = 1 and B = 0. Which expression gives X = 1?
A. NOT (A AND B) ✓
B. (NOT A) AND B
NOT (A AND B): 1 AND 0 = 0, NOT 0 = 1. (NOT A) AND B: NOT 1 = 0, then 0 AND 0 = 0. The two expressions give different results.

Match the Pairs

(NOT A) AND B → NOT flips only input A first. The result of that is then ANDed with B.
NOT (A AND B) → A AND B is worked out first. NOT then flips the whole result of the bracket.
NOT applies to the input A alone, and B is not changed before the AND → X = (NOT A) AND B
NOT is applied to the output of an AND gate, so it flips the result of the bracket → X = NOT (A AND B)
X = NOT A AND B (meant: NOT (A AND B)) → The brackets are missing, so NOT applies only to A. The student wanted NOT to flip the whole result of A AND B.
X = NOT (A AND B) (meant: (NOT A) AND B) → The brackets are placed round A AND B, so NOT flips the final output. The student wanted NOT on input A only.

Key Term

NOT (A AND B)
NOT before a bracket flips the whole bracket's result. In (NOT A) AND B, NOT flips only input A, so NOT (A AND B) gives different results.

Fill in the Blanks

1. X = NOT (A AND B)
Hint: Type the gate keyword placed before the bracket so it flips the whole bracket's result.
2. X = (NOT A) AND B
Hint: Type the gate that combines the result of NOT A with input B.
3. X = (NOT A) AND B
Hint: Type the input letter that NOT flips on its own, the one named first in the expression.
4. When A = 1 and B = 0: NOT (A AND B) = 1
Hint: Work out A AND B first, then flip that bracket result. Type the final output bit.
5. When A = 1 and B = 0: (NOT A) AND B = 0
Hint: Flip only input A, then AND the result with B. Type the final output bit.

Spot the Error

Question 1
A # A=1, B=0, so X must be 1
B X = (NOT A) AND B
C # bracket = 0, NOT gives 1
Line B — NOT must go before the bracket so it flips the whole result of A AND B. (NOT A) AND B only flips A, giving 0 here instead of 1. It should be X = NOT (A AND B).
Question 2
A # A=1, B=0, so X must be 0
B # NOT flips only input A
C X = NOT (A AND B)
Line C — The comment says NOT applies to input A only, so A needs its own brackets: (NOT A) AND B. NOT (A AND B) flips the whole bracket and gives 1, not 0.
Question 3
A a = True
B b = False
C x = not a and b
D print(x) # True
Line C — Without brackets, not applies only to a, so the result is False. To flip the whole result of a and b, write x = not (a and b), which gives True.
Question 4
A A = 0, B = 0
B A AND B = 0
C NOT (A AND B) = 1
D (NOT A) AND B = 1
Line D — NOT A is 1 and B is 0, so 1 AND 0 = 0. The answer should be (NOT A) AND B = 0, which differs from NOT (A AND B) = 1.
Question 5
A A = 1, B = 1
B A AND B = 1
C NOT (A AND B) = 1
D (NOT A) AND B = 0
Line C — A AND B is 1, and NOT flips the bracket's result, so NOT (A AND B) = 0, not 1.

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