← IGCSE Computer Science Paper 2

Limits on circuit size: three inputs and one output

A circuit here has at most three inputs (A, B, C) and exactly one output X. With 3 inputs the truth table has 8 rows (2 x 2 x 2). Gates with two inputs can be combined to handle the third input.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 38

Understanding Limits on circuit size: three inputs and one output in IGCSE Computer Science Paper 2

What it does: Each input can be 0 or 1, so three inputs give 2 x 2 x 2 = 8 different input combinations, one per row. Circuits in 0478 have at most three inputs, labelled A, B and C. Every circuit has a single output, labelled X. Each input has 2 values, so the rows are 2 x 2 x 2 = 8. A NOT circuit has 1 input and an AND circuit has 2. The limit is a maximum of three, not a fixed number. There is one output, so we write a single X. These gates have two inputs, so two-input gates are combined to handle the third input. Only a NOT gate has one input.

Common mistakes: Circuits in this course have at most three inputs (A, B and C). There is no fourth input D. The line should be 'Inputs: A, B, C'. A circuit has exactly one output, called X. There is no second output Y. The line should be 'Output: X'.

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This module's key terms are also in a printable crossword (Modules 562–580) and word search (Modules 539–580).

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Learning
Duo
What is the maximum number of inputs a circuit has in this course?
4 inputs: A, B, C and D3 inputs: A, B and C
Matches
A circuit with inputs A, B, C, D and two outputs X and Y
↓
Too many inputs and outputs: circuits here have at most three inputs (A, B, C) and exactly one output X.
Applying
Meanings
Term
3 inputs, 1 output
Meaning
A circuit here has at most three inputs (A, B, C) and exactly one output X. With 3 inputs the truth table has 8 rows (2 x 2 x 2). Gates with two inputs can be combined to handle the third input.
Practice
Inputs: A, B, C
Testing
Gaps
X = (A AND B) OR
Check Answer
Spots
1Inputs: A, B, C, D
2Output: X

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Quick Questions

1. What is the maximum number of inputs a circuit has in this course?
A. 3 inputs: A, B and C ✓
B. 4 inputs: A, B, C and D
Circuits in 0478 have at most three inputs, labelled A, B and C.
2. How many outputs does a circuit in this course have?
A. Exactly one output, X ✓
B. Two outputs, X and Y
Every circuit has a single output, labelled X.
3. How many rows does a truth table with 3 inputs have?
A. 8 rows ✓
B. 6 rows
Each input has 2 values, so the rows are 2 x 2 x 2 = 8.
4. How many rows does a truth table with 2 inputs have?
A. 8 rows
B. 4 rows ✓
Two inputs give 2 x 2 = 4 input combinations. Only three inputs give 8 rows.
5. Which statement about circuit size is correct?
A. A circuit must always have 3 inputs
B. A circuit can have 1, 2 or 3 inputs ✓
A NOT circuit has 1 input and an AND circuit has 2. The limit is a maximum of three, not a fixed number.

Match the Pairs

A, B, C → The most inputs a circuit can have in this course: three, labelled A, B and C
X → The single output of a circuit; there is always exactly one
A circuit with three inputs has a truth table with 2 x 2 x 2 = 8 rows → 2 x 2 x 2 = 8
Two-input gates can be combined to handle a third input, with one output X → X = (A AND B) OR C
A circuit with inputs A, B, C, D and two outputs X and Y → Too many inputs and outputs: circuits here have at most three inputs (A, B, C) and exactly one output X.
Three inputs A, B, C: the truth table has 6 rows → Wrong row count: three inputs give 2 x 2 x 2 = 8 rows, not 6.

Key Term

3 inputs, 1 output
A circuit here has at most three inputs (A, B, C) and exactly one output X. With 3 inputs the truth table has 8 rows (2 x 2 x 2). Gates with two inputs can be combined to handle the third input.

Fill in the Blanks

1. X = (A AND B) OR C
Hint: Type the letter of the third input, the one that is not A or B.
2. Rows = 2 x 2 x 2 = 8
Hint: Type the number of rows in a truth table with three inputs.
3. X = (A AND B) AND C
Hint: Type the gate that makes X equal 1 only when all three inputs are 1.
4. Inputs: A, B, C Output: X
Hint: Type the letter used for the one and only output.
5. Inputs: A, B Rows: 2 x 2 = 4
Hint: Type the number of rows in a truth table with two inputs.

Spot the Error

Question 1
A Inputs: A, B, C, D
B Output: X
C Rows in truth table: 8
Line A — Circuits in this course have at most three inputs (A, B and C). There is no fourth input D. The line should be 'Inputs: A, B, C'.
Question 2
A Inputs: A, B
B Outputs: X, Y
C Rows in truth table: 4
Line B — A circuit has exactly one output, called X. There is no second output Y. The line should be 'Output: X'.
Question 3
A Inputs: A, B, C
B Rows: 2 x 2 x 2 = 6
C Output: X
Line B — Each of the 3 inputs can be 0 or 1, so the table has 2 x 2 x 2 = 8 rows, not 6.
Question 4
A Inputs: A
B Output: X
C Rows in truth table: 4
Line C — One input can only be 0 or 1, so the truth table has 2 rows. Four rows would need two inputs.
Question 5
A Inputs: A, B, C
B Each gate here has 2 inputs
C X = (A AND B) OR D
Line C — D is not an input, because the only inputs are A, B and C. The expression should end with OR C. The two-input gates combine to bring in the third input.

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