Truth table layout for three inputs

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Truth table layout for three inputs

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. How many rows does a truth table with three inputs A, B and C have?
A 8 rows
B 6 rows
2. Which calculation gives the number of rows for three inputs?
A 3 x 2
B 2 x 2 x 2
3. What is the first row of a three-input truth table (A B C)?
A 0 0 1
B 0 0 0
4. Which row comes straight after 0 1 1 in binary counting order?
A 1 0 0
B 1 1 1
5. Which input changes slowest down the rows of the table?
A A
B C
B

Match the Pairs

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

Left columnRight column
1000, 001, 010, 011, 100, 101, 110, 111 AC: 0 1 0 1 0 1 0 1
22 x 2 x 2 = 8 BA: 0 0 0 0 1 1 1 1
3A changes slowest: the A column is four 0s and then four 1s CThe table stops at 101, so rows 110 and 111 are missing. A three-input truth table needs all 8 rows, ending at 111.
4C changes fastest: the C column alternates 0 and 1 on every row DThe eight input rows of a three-input truth table, written in binary counting order
5A B C rows: 000, 001, 010, 011, 100, 101 (6 rows) EThe number of rows needed for a truth table with three inputs
6A B C rows: 000, 010, 001, 011, 100, 110, 101, 111 FThe rows are not in binary counting order: 010 comes before 001, and 110 comes before 101. C should change fastest.
C

Definitions

000 to 111
D

Fill in the Blanks

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

1.
rows = 2 ^ _ = 8
2.
000 001 ___
3.
First row: 000 Last row: ___
4.
A is 0 for the first _ rows A is 1 for the last 4 rows
5.
Fastest changing column: _ Slowest changing column: A
E

Spot the Error

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

Question 1
A A B C
B 0 1 0
C 0 0 1
D 0 1 0
Question 2
A A B C
B 0 0 0
C 1 0 0
D 0 1 0
E 0 1 1
Question 3
A inputs ← 3
B rows ← 2 * inputs
C OUTPUT rows
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
Question 5
A Three inputs give 6 rows
B The first row is 0 0 0
C The last row is 1 1 1

Answer Key

Truth table layout for three inputs
Section A: Quick Questions
Q1
A — 8 rows
Q2
B — 2 x 2 x 2
Q3
B — 0 0 0
Q4
A — 1 0 0
Q5
A — A
Section B: Match the Pairs
Q1
000, 001, 010, 011, 100, 101, 110, 111 → The eight input rows of a three-input truth table, written in binary counting order
Q2
2 x 2 x 2 = 8 → The number of rows needed for a truth table with three inputs
Q3
A changes slowest: the A column is four 0s and then four 1s → A: 0 0 0 0 1 1 1 1
Q4
C changes fastest: the C column alternates 0 and 1 on every row → C: 0 1 0 1 0 1 0 1
Q5
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.
Q6
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.
Section C: Definitions
Q1
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.
Section D: Fill in the Blanks
Q1
rows = 2 ^ 3 = 8
Q2
000 001 010
Q3
First row: 000 Last row: 111
Q4
A is 0 for the first 4 rows A is 1 for the last 4 rows
Q5
Fastest changing column: C Slowest changing column: A
Section E: Spot the Error
Q1
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.
Q2
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.
Q3
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.
Q4
C — A changes slowest, so it stays 0 for the first four rows. Row 3 should be A=0 B=1 C=0.
Q5
A — Three inputs give 2 x 2 x 2 = 8 rows, not 6. It should say 8 rows.