← IGCSE Computer Science Paper 2

OR versus XOR: the row where both inputs are 1

Exclusive OR: outputs 1 when exactly one input is 1. When A and B are both 1 it outputs 0, but OR outputs 1 in that row. XOR means one or the other, but not both.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 14

Understanding OR versus XOR: the row where both inputs are 1 in IGCSE Computer Science Paper 2

What it does: This row shows OR giving 1 and XOR giving 0, while all other rows have the same outputs. The phrase 'but not both' excludes the both-1 row, so the gate is XOR rather than OR. OR outputs 1 when at least one input is 1, so the row 1 and 1 gives 1. XOR means one or the other but not both. With both inputs 1, the output is 0. The OR and XOR columns match in every row except A = 1, B = 1. OR gives 1 and XOR gives 0. 'At least one' describes OR (inclusive). XOR is exclusive: exactly one input must be 1.

Common mistakes: The results show X=0 when both inputs are 1, which is XOR behaviour. OR would output 1 in that row. The line should be X = A XOR B. When A and B are both 1, OR outputs 1 but XOR outputs 0, because XOR means one or the other but not both. The row should be 1 1 | 1 | 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

A = 1 and B = 1. What does an OR gate output?

Matches

A B | XOR 1 1 | 1

↓

XOR is shown outputting 1 when both inputs are 1. XOR must output 0 in this row because it needs exactly one input to be 1.

Applying

Meanings

Term

XOR

Meaning

Exclusive OR: outputs 1 when exactly one input is 1. When A and B are both 1 it outputs 0, but OR outputs 1 in that row. XOR means one or the other, but not both.

Practice

A B OR XOR

Testing

Gaps

X = A B

Check Answer

Spots

1X = A OR B

2A=1, B=1 -> X=0

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Quick Questions

1. A = 1 and B = 1. What does an OR gate output?

A. 1 ✓

B. 0

OR outputs 1 when at least one input is 1, so the row 1 and 1 gives 1.

2. A = 1 and B = 1. What does an XOR gate output?

A. 1

B. 0 ✓

XOR means one or the other but not both. With both inputs 1, the output is 0.

3. Which gate gives a different output from OR only in the row where A = 1 and B = 1?

A. XOR ✓

B. AND

The OR and XOR columns match in every row except A = 1, B = 1. OR gives 1 and XOR gives 0.

4. Which statement describes XOR correctly?

A. Outputs 1 when exactly one input is 1 ✓

B. Outputs 1 when at least one input is 1

'At least one' describes OR (inclusive). XOR is exclusive: exactly one input must be 1.

5. A shop sign says 'You may have a free drink or a free snack, but not both.' Which gate matches this wording?

A. OR

B. XOR ✓

'Either...or, but not both' is exclusive, so it matches XOR. OR would also allow both.

Match the Pairs

A = 1, B = 1, A OR B → Outputs 1, because OR is inclusive and accepts one input or both inputs being 1

A = 1, B = 1, A XOR B → Outputs 0, because XOR is exclusive and needs exactly one input to be 1

The only row where the OR and XOR output columns differ is the row where both inputs are 1 → A B | OR XOR 1 1 | 1 0

Everyday 'either...or but not both' wording describes XOR, for example you can have tea or coffee but not both → X = A XOR B

A B | XOR 1 1 | 1 → XOR is shown outputting 1 when both inputs are 1. XOR must output 0 in this row because it needs exactly one input to be 1.

A B | OR 1 1 | 0 → OR is shown outputting 0 when both inputs are 1. OR is inclusive, so it must output 1 whenever at least one input is 1, including both.

Key Term

XOR

Exclusive OR: outputs 1 when exactly one input is 1. When A and B are both 1 it outputs 0, but OR outputs 1 in that row. XOR means one or the other, but not both.

Fill in the Blanks

1. X = A XOR B

Hint: Type the gate name that means one or the other, but not both.

2. X = A OR B A = 1, B = 1 X = 1

Hint: Type the output of an OR gate when both inputs are 1.

3. A = 1, B = 1 X = A XOR B X = 0

Hint: Type the output of an XOR gate when both inputs are 1.

4. A B OR XOR 1 1 1 0

Hint: Type the OR output in the row where both inputs are 1.

5. Tea or coffee, or both: X = A OR B

Hint: Type the gate that matches an inclusive 'or both' meaning.

Spot the Error

Question 1

A X = A OR B

B A=1, B=1 -> X=0

C A=1, B=0 -> X=1

D A=0, B=0 -> X=0

Line A — The results show X=0 when both inputs are 1, which is XOR behaviour. OR would output 1 in that row. The line should be X = A XOR B.

Question 2

A A B | OR | XOR

B 0 0 | 0 | 0

C 1 1 | 1 | 1

D 1 0 | 1 | 1

Line C — When A and B are both 1, OR outputs 1 but XOR outputs 0, because XOR means one or the other but not both. The row should be 1 1 | 1 | 0.

Question 3

A A <- 1

B B <- 1

C X <- A OR B

D OUTPUT X // prints 0

Line C — With A and B both 1, OR would give 1, but the program expects 0. It should use XOR: X <- A XOR B.

Question 4

A Either tea or coffee, not both

B Gate needed: XOR

C Tea and coffee both 1: X = 1

D Only tea is 1: X = 1

Line C — 'Either...or, not both' describes XOR. When both inputs are 1, XOR outputs 0, so the line should say X = 0.

Question 5

A OR gate, inputs A and B

B A=1, B=1 gives X=0

C A=1, B=0 gives X=1

D A=0, B=0 gives X=0

Line B — OR is inclusive, so it outputs 1 when both inputs are 1. The line should be A=1, B=1 gives X=1.

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