Limits on circuit size: three inputs and one output

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Date:

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Quick Questions

Shade in the A or B circle for each question.

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

2. How many outputs does a circuit in this course have?

A Exactly one output, X

B Two outputs, X and Y

3. How many rows does a truth table with 3 inputs have?

A 8 rows

B 6 rows

4. How many rows does a truth table with 2 inputs have?

A 8 rows

B 4 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

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1A, B, C		AToo many inputs and outputs: circuits here have at most three inputs (A, B, C) and exactly one output X.
2X		BThe single output of a circuit; there is always exactly one
3A circuit with three inputs has a truth table with 2 x 2 x 2 = 8 rows		CThe most inputs a circuit can have in this course: three, labelled A, B and C
4Two-input gates can be combined to handle a third input, with one output X		DX = (A AND B) OR C
5A circuit with inputs A, B, C, D and two outputs X and Y		E2 x 2 x 2 = 8
6Three inputs A, B, C: the truth table has 6 rows		FWrong row count: three inputs give 2 x 2 x 2 = 8 rows, not 6.

Definitions

3 inputs, 1 output

Fill in the Blanks

Complete each line of code by filling in the missing parts.

X = (A AND B) OR _

Rows = 2 x 2 x 2 = _

X = (A AND B) ___ C

Inputs: A, B, C Output: _

Inputs: A, B Rows: 2 x 2 = _

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A Inputs: A, B, C, D

B Output: X

C Rows in truth table: 8

Question 2

A Inputs: A, B

B Outputs: X, Y

C Rows in truth table: 4

Question 3

A Inputs: A, B, C

B Rows: 2 x 2 x 2 = 6

C Output: X

Question 4

A Inputs: A

B Output: X

C Rows in truth table: 4

Question 5

A Inputs: A, B, C

B Each gate here has 2 inputs

C X = (A AND B) OR D

Answer Key

Limits on circuit size: three inputs and one output

Section A: Quick Questions

A — 3 inputs: A, B and C

A — Exactly one output, X

A — 8 rows

B — 4 rows

B — A circuit can have 1, 2 or 3 inputs

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

X = (A AND B) OR C

Rows = 2 x 2 x 2 = 8

X = (A AND B) AND C

Inputs: A, B, C
Output: X

Inputs: A, B
Rows: 2 x 2 = 4

Section E: Spot the Error

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'.

B — A circuit has exactly one output, called X. There is no second output Y. The line should be 'Output: X'.

B — Each of the 3 inputs can be 0 or 1, so the table has 2 x 2 x 2 = 8 rows, not 6.

C — One input can only be 0 or 1, so the truth table has 2 rows. Four rows would need two inputs.

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.