← IGCSE Computer Science Paper 2

Truth table layout for three inputs

A three-input truth table has 8 rows (2 x 2 x 2) in binary counting order from 000 to 111, with A changing slowest and C changing fastest.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 20

Understanding Truth table layout for three inputs in IGCSE Computer Science Paper 2

What it does: A is the leftmost input, so it is the most significant bit and only switches once, halfway down the table. C is the rightmost input, so it is the least significant bit and flips on every row. Each input has 2 values, so there are 2 x 2 x 2 = 2^3 = 8 combinations. Adding two inputs gives 8, not 6. Each input can be 0 or 1, so you multiply 2 once for each input: 2 x 2 x 2 = 8. Binary counting order starts at 000 and ends at 111, so the first row is always 0 0 0.

Common mistakes: The first row of a three-input truth table must be 0 0 0, because the binary count starts at zero. It should be 0 0 0. After 0 0 1 the next binary number is 0 1 0. C changes fastest and A changes slowest, so A cannot jump to 1 this early. It should be 0 1 0.

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Learning
Duo
How many rows does a truth table with three inputs A, B and C have?
6 rows8 rows
Matches
A B C rows: 000, 001, 010, 011, 100, 101 (6 rows)
↓
The table stops at 101, so rows 110 and 111 are missing. A three-input truth table needs all 8 rows, ending at 111.
Applying
Meanings
Term
000 to 111
Meaning
A three-input truth table has 8 rows (2 x 2 x 2) in binary counting order from 000 to 111, with A changing slowest and C changing fastest.
Practice
A B C
Testing
Gaps
rows = 2 ^ = 8
Check Answer
Spots
1A B C
20 1 0

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Quick Questions

1. How many rows does a truth table with three inputs A, B and C have?
A. 8 rows ✓
B. 6 rows
Each input has 2 values, so there are 2 x 2 x 2 = 2^3 = 8 combinations. Adding two inputs gives 8, not 6.
2. Which calculation gives the number of rows for three inputs?
A. 3 x 2
B. 2 x 2 x 2 ✓
Each input can be 0 or 1, so you multiply 2 once for each input: 2 x 2 x 2 = 8.
3. What is the first row of a three-input truth table (A B C)?
A. 0 0 1
B. 0 0 0 ✓
Binary counting order starts at 000 and ends at 111, so the first row is always 0 0 0.
4. Which row comes straight after 0 1 1 in binary counting order?
A. 1 0 0 ✓
B. 1 1 1
Counting in binary: 011 is 3, so the next number is 4, which is 100. The jump to 111 skips rows.
5. Which input changes slowest down the rows of the table?
A. A ✓
B. C
A is the leftmost column. It stays 0 for the first 4 rows, then 1 for the last 4 rows. C changes fastest.

Match the Pairs

000, 001, 010, 011, 100, 101, 110, 111 → The eight input rows of a three-input truth table, written in binary counting order
2 x 2 x 2 = 8 → The number of rows needed for a truth table with three inputs
A changes slowest: the A column is four 0s and then four 1s → A: 0 0 0 0 1 1 1 1
C changes fastest: the C column alternates 0 and 1 on every row → C: 0 1 0 1 0 1 0 1
A B C rows: 000, 001, 010, 011, 100, 101 (6 rows) → The table stops at 101, so rows 110 and 111 are missing. A three-input truth table needs all 8 rows, ending at 111.
A B C rows: 000, 010, 001, 011, 100, 110, 101, 111 → The rows are not in binary counting order: 010 comes before 001, and 110 comes before 101. C should change fastest.

Key Term

000 to 111
A three-input truth table has 8 rows (2 x 2 x 2) in binary counting order from 000 to 111, with A changing slowest and C changing fastest.

Fill in the Blanks

1. rows = 2 ^ 3 = 8
Hint: Type the number of inputs (A, B and C) that is used as the power.
2. 000 001 010
Hint: Type the next three-bit binary row after 001 in counting order.
3. First row: 000 Last row: 111
Hint: Type the final row, where every input is at its highest value.
4. A is 0 for the first 4 rows A is 1 for the last 4 rows
Hint: Type how many rows A stays the same before it changes (half of 8).
5. Fastest changing column: C Slowest changing column: A
Hint: Type the input letter that flips every single row.

Spot the Error

Question 1
A A B C
B 0 1 0
C 0 0 1
D 0 1 0
Line B — The first row of a three-input truth table must be 0 0 0, because the binary count starts at zero. It should be 0 0 0.
Question 2
A A B C
B 0 0 0
C 1 0 0
D 0 1 0
E 0 1 1
Line C — After 0 0 1 the next binary number is 0 1 0. C changes fastest and A changes slowest, so A cannot jump to 1 this early. It should be 0 1 0.
Question 3
A inputs ← 3
B rows ← 2 * inputs
C OUTPUT rows
Line B — The number of rows is 2 raised to the power of the number of inputs (2^3 = 8). Multiplying 2 by 3 gives 6 rows, which is wrong. It should be rows ← 2 ^ inputs.
Question 4
A Row 1: A=0 B=0 C=0
B Row 2: A=0 B=0 C=1
C Row 3: A=1 B=0 C=0
D Row 4: A=0 B=1 C=1
Line C — A changes slowest, so it stays 0 for the first four rows. Row 3 should be A=0 B=1 C=0.
Question 5
A Three inputs give 6 rows
B The first row is 0 0 0
C The last row is 1 1 1
Line A — Three inputs give 2 x 2 x 2 = 8 rows, not 6. It should say 8 rows.

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