Identifying a gate from its truth table output

Read the output column for rows 00, 01, 10, 11 to name the gate: AND 0001, OR 0111, NAND 1110, NOR 1000, XOR 0110.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 16

Understanding Identifying a gate from its truth table output in IGCSE Computer Science Paper 2

What it does: NOR is the opposite of OR. Only row 00 gives 1, so the output column is 1000. XOR outputs 1 only when exactly one input is 1 (rows 01 and 10), giving 0110. AND has its single 1 in row 11 (0001). A single 1 in row 00 means NOR. The broken code gives the AND column for OR. OR is 0111.

Common mistakes: NAND has the output column 1110, so row 01 must give 1. The line should be 0 1 1. The output column 0111 is an OR gate. XOR has 0110 because row 11 gives 0. It should be Gate: OR.

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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 gate's output column for rows 00, 01, 10, 11 is 0001. Which gate is it?

ANDOR

Matches

OR gate output column: 0001

↓

0001 is the AND pattern, not OR. OR outputs 1 whenever at least one input is 1, so it should be 0111.

Applying

Meanings

Term

output column

Meaning

Read the output column for rows 00, 01, 10, 11 to name the gate: AND 0001, OR 0111, NAND 1110, NOR 1000, XOR 0110.

Practice

// rows 00 01 10 11

Testing

Gaps

Output column 0001 is the gate

Check Answer

Spots

20 0 1

30 1 0

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Quick Questions

1. A gate's output column for rows 00, 01, 10, 11 is 0001. Which gate is it?

A. AND ✓

B. OR

AND gives 1 only when both inputs are 1, so only row 11 outputs 1: 0001.

2. A gate's output column is 0111. Which gate is it?

A. XOR

B. OR ✓

OR outputs 1 whenever at least one input is 1, including row 11. XOR would give 0 in row 11 (0110).

3. A gate's output column is 0110. Which gate is it?

A. XOR ✓

B. OR

XOR outputs 1 only when the inputs are different, so rows 01 and 10 give 1 and row 11 gives 0.

4. A gate's output column is 1110. Which gate is it?

A. NOR

B. NAND ✓

NAND is the opposite of AND (0001), so it outputs 1110. Only row 11 gives 0.

5. A gate's output column is 1000. Which gate is it?

A. NOR ✓

B. NAND

NOR is the opposite of OR (0111), so it outputs 1000. It gives 1 only when both inputs are 0.

Match the Pairs

Output column 0001 (rows 00, 01, 10, 11) → This is an AND gate

Output column 1110 (rows 00, 01, 10, 11) → This is a NAND gate

The output is 1 only when both inputs are 0, so the column reads 1, 0, 0, 0 → NOR = 1000

The output is 1 when the inputs are different, so the column reads 0, 1, 1, 0 → XOR = 0110

OR gate output column: 0001 → 0001 is the AND pattern, not OR. OR outputs 1 whenever at least one input is 1, so it should be 0111.

NOR gate output column: 0111 → 0111 is the OR pattern. NOR is the opposite of OR, so it should be 1000.

Key Term

output column

Read the output column for rows 00, 01, 10, 11 to name the gate: AND 0001, OR 0111, NAND 1110, NOR 1000, XOR 0110.

Fill in the Blanks

1. Output column 0001 is the AND gate

Hint: Type the name of the gate whose output column is 0001

2. NOR output for 00, 01, 10, 11: 1000

Hint: Type the four-digit output column for the NOR gate

3. Rows 00 01 10 11 give X = 0110 This is the XOR gate

Hint: Type the gate name that matches this output column, where the output is 1 only when the inputs differ

4. Output 0001: only row 11 gives X = 1

Hint: Type the row (the A and B values) where the AND gate outputs 1

5. X column for rows 00 01 10 11: 0111 Gate name: OR

Hint: Type the gate name that matches this output column, where the output is 1 unless both inputs are 0

Spot the Error

Question 1

A A B X

B 0 0 1

C 0 1 0

D 1 0 1

E 1 1 0

F Gate: NAND

Line C — NAND has the output column 1110, so row 01 must give 1. The line should be 0 1 1.

Question 2

A Output column: 0111

B Row 00 gives 0

C Rows 01, 10, 11 give 1

D Gate: XOR

Line D — The output column 0111 is an OR gate. XOR has 0110 because row 11 gives 0. It should be Gate: OR.

Question 3

A Output column: 1000

B Only row 11 gives 1

C Gate: NOR

Line B — NOR (1000) gives 1 only when both inputs are 0, which is row 00. The line should be Only row 00 gives 1.

Question 4

A Output column: 0110

B Rows 00 and 11 give 1

C Gate: XOR

Line B — XOR (0110) gives 1 only when the inputs are different, so rows 01 and 10 give 1. The line should be Rows 01 and 10 give 1.

Question 5

A A B X

B 0 0 0

C 0 1 1

D 1 0 0

E 1 1 1

F Gate: AND

Line C — AND (0001) gives 1 only for row 11, so row 01 must give 0. The line should be 0 1 0.

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