← IGCSE Computer Science Paper 2

Brackets in logic expressions

Brackets show which gate is worked out first. Here A AND B is done first, then its result goes into OR with C. A AND (B OR C) uses the same letters but gives a different output.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 18

Understanding Brackets in logic expressions in IGCSE Computer Science Paper 2

What it does: The innermost bracket (A AND B) is done first, then the OR bracket, and the NOT is applied last to that result. B OR C gives 1, but then 0 AND 1 gives 0. With (A AND B) OR C the same inputs would give 1. There is one gate for each operator. The letters are inputs, not gates. AND and OR are the two operators, so there are 2 gates. Brackets first: 0 AND 0 = 0. Then 0 OR 1 = 1. The brackets go around the gate that must be worked out first. Here that is A OR B, so (A OR B) AND C is correct.

Common mistakes: The inner bracket is worked out first. With A = 1 and B = 0, A AND B = 0, not 1, because AND needs both inputs to be 1. The bracket B OR C is worked out first. With B = 1 and C = 1, OR gives 1, not 0, because OR outputs 1 when at least one input is 1.

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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 (A AND B) OR C, which gate is worked out first?

OR, because it is written lastAND, because it is inside the brackets

Matches

X = A AND B OR C

↓

There are no brackets, so it is unclear which gate is worked out first. It needs brackets such as (A AND B) OR C or A AND (B OR C).

Applying

Meanings

Term

(A AND B) OR C

Meaning

Brackets show which gate is worked out first. Here A AND B is done first, then its result goes into OR with C. A AND (B OR C) uses the same letters but gives a different output.

Practice

X = (A AND B) OR C

Testing

Gaps

X = (A B) OR C

Check Answer

Spots

2X = (A AND B) OR C

3Inner bracket: A AND B = 1

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Quick Questions

1. In (A AND B) OR C, which gate is worked out first?

A. OR, because it is written last

B. AND, because it is inside the brackets ✓

The inner brackets are always worked out first. A AND B is done first, then its result goes into the OR gate with C.

2. How many gates are in the expression (A AND B) OR C?

A. 2 gates: one AND and one OR ✓

B. 3 gates: one for each input letter

There is one gate for each operator. The letters are inputs, not gates. AND and OR are the two operators, so there are 2 gates.

3. True or false: (A AND B) OR C and A AND (B OR C) always give the same output.

A. True: they use the same letters and the same gates

B. False: moving the brackets changes which gate is done first ✓

Same letters and gates can still give different outputs. For A=0, B=0, C=1 the first gives 1 and the second gives 0.

4. A=0, B=0, C=1. What is the output of (A AND B) OR C?

A. 1 ✓

B. 0

Brackets first: 0 AND 0 = 0. Then 0 OR 1 = 1.

5. A=0, B=0, C=1. What is the output of A AND (B OR C)?

A. 0 ✓

B. 1

Brackets first: 0 OR 1 = 1. Then 0 AND 1 = 0. This differs from (A AND B) OR C for the same inputs.

Match the Pairs

X = (A AND B) OR C → A AND B is worked out first, then its result goes into OR with C

X = A AND (B OR C) → B OR C is worked out first, then its result goes into AND with A

Inner brackets are worked out first: A AND B, then OR with C, then the whole result is inverted by NOT → X = NOT ((A AND B) OR C)

Same letters with different brackets can give a different output: when A=0, B=0 and C=1 this expression gives 0 → X = A AND (B OR C)

X = A AND B OR C → There are no brackets, so it is unclear which gate is worked out first. It needs brackets such as (A AND B) OR C or A AND (B OR C).

X = (A AND (B OR C) → A closing bracket is missing, so the brackets do not pair up. It should be X = A AND (B OR C) or X = (A AND (B OR C)).

Key Term

(A AND B) OR C

Brackets show which gate is worked out first. Here A AND B is done first, then its result goes into OR with C. A AND (B OR C) uses the same letters but gives a different output.

Fill in the Blanks

1. X = (A AND B) OR C

Hint: Type the gate inside the brackets, which is worked out first.

2. X = A AND (B OR C)

Hint: Type the gate inside the brackets that is worked out before the AND.

3. A = 1, B = 0, C = 1 (A AND B) OR C = 1

Hint: Type the output bit: work out the bracket first, then use OR with C.

4. A = 0, B = 1, C = 1 (A AND B) OR C = 1 A AND (B OR C) = 0

Hint: Type the output bit when the brackets are moved: B OR C is done first.

5. X = (A AND B) OR C Step 1: P = A AND B Step 2: X = P OR C

Hint: Type the input that joins the bracket result P in the second gate.

Spot the Error

Question 1

A A = 1, B = 0, C = 1

B X = (A AND B) OR C

C Inner bracket: A AND B = 1

D X = 0 OR 1 = 1

Line C — The inner bracket is worked out first. With A = 1 and B = 0, A AND B = 0, not 1, because AND needs both inputs to be 1.

Question 2

A A = 0, B = 1, C = 1

B X = A AND (B OR C)

C Inner bracket B OR C = 0

D X = 0 AND 1 = 0

Line C — The bracket B OR C is worked out first. With B = 1 and C = 1, OR gives 1, not 0, because OR outputs 1 when at least one input is 1.

Question 3

A A = 1, B = 1, C = 0

B X = (A AND B) OR C

C A AND B = 1

D X = 1 OR 0 = 0

Line D — The result of the bracket (1) goes into OR with C (0). 1 OR 0 = 1, because OR outputs 1 when at least one input is 1. So X = 1, not 0.

Question 4

A X = A AND (B OR C)

B Work out B OR C first

C Then A OR the result

Line C — The expression is A AND (B OR C). After the bracket is worked out, its result goes into an AND gate with A, not an OR gate.

Question 5

A A = 1, B = 0, C = 0

B (A OR B) AND C: A OR B = 0

C then 1 AND C = 1 AND 0 = 0

Line B — The bracket is worked out first. A OR B with A = 1 and B = 0 gives 1, not 0, because OR outputs 1 when at least one input is 1.

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