Completing a truth table from an expression: three inputs

Tip: Choose Save as PDF in the print dialog to download. Use A4 paper size.

Completing a truth table from an expression: three inputs

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. A truth table for the three inputs A, B and C needs how many rows?
A 8 rows
B 6 rows
2. In X = (A AND B) OR C, which part do you work out first?
A The bracket (A AND B), in its own column
B The OR with C, then the AND
3. For X = (A AND B) OR C, what is X when A = 1, B = 1 and C = 0?
A X = 0
B X = 1
4. For X = (A AND B) OR C, what is X when A = 1, B = 0 and C = 0?
A X = 1
B X = 0
5. In X = (A AND B) OR C, a row has C = 1. What is X in that row?
A X = 1, whatever A and B are
B X = 0 unless A AND B is 1
B

Match the Pairs

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

Left columnRight column
1X = (A AND B) OR C AA=1 B=1 C=0: (1 AND 1) = 1, 1 OR 0 = 1, X = 1
2X = (A XOR B) AND C BWork out A AND B first in an extra column, then OR that result with C in all 8 rows.
3A three-input truth table has 2 x 2 x 2 = 8 rows, counting from 000 to 111 in A, B, C order. CThe bracket result was combined with C using AND, but the expression uses OR. It should be 0 OR 1 = 1, so X = 1.
4For X = (A AND B) OR C, the row A=1, B=1, C=0 gives X = 1 because the bracket result is 1. D1 AND 0 is 0, not 1, because AND needs both inputs to be 1. The correct working is 0 OR 0 = 0, so X = 0.
5A=0 B=1 C=1: (0 AND 1) = 0, 0 AND 1 = 0, X = 0 E000, 001, 010, 011, 100, 101, 110, 111
6A=1 B=0 C=0: (1 AND 0) = 1, 1 OR 0 = 1, X = 1 FWork out A XOR B first in an extra column. X is 1 only when that column is 1 and C is 1.
C

Definitions

X = (A AND B) OR C
D

Fill in the Blanks

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

1.
X = (A ___ B) OR C
2.
X = (A AND B) __ C
3.
Rows needed: 2 x 2 x 2 = _
4.
A=1, B=1, C=0: P = A AND B = 1 X = P OR C = _
5.
X = (A XOR B) AND ___ C
E

Spot the Error

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

Question 1
A X = (A AND B) OR C
B Rows needed: 2^3 = 6
C Extra column: D = A AND B
D Output column: X = D OR C
Question 2
A X = (A AND B) OR C
B Row: A=1, B=1, C=0
C A AND B = 0
D X = 1 OR 0 = 1
Question 3
A X = (A OR B) AND C
B Row: A=1, B=0, C=0
C A OR B = 0
D X = 1 AND 0 = 0
Question 4
A X = (NOT A) OR (B AND C)
B Row: A=1, B=1, C=0
C NOT A = 1, B AND C = 0
D X = 0 OR 0 = 0
Question 5
A X = (A XOR B) AND C
B Row: A=1, B=1, C=1
C Intermediate: A XOR B = 0
D X = 0 AND 1 = 1

Answer Key

Completing a truth table from an expression: three inputs
Section A: Quick Questions
Q1
A — 8 rows
Q2
A — The bracket (A AND B), in its own column
Q3
B — X = 1
Q4
B — X = 0
Q5
A — X = 1, whatever A and B are
Section B: Match the Pairs
Q1
X = (A AND B) OR C → Work out A AND B first in an extra column, then OR that result with C in all 8 rows.
Q2
X = (A XOR B) AND C → Work out A XOR B first in an extra column. X is 1 only when that column is 1 and C is 1.
Q3
A three-input truth table has 2 x 2 x 2 = 8 rows, counting from 000 to 111 in A, B, C order. → 000, 001, 010, 011, 100, 101, 110, 111
Q4
For X = (A AND B) OR C, the row A=1, B=1, C=0 gives X = 1 because the bracket result is 1. → A=1 B=1 C=0: (1 AND 1) = 1, 1 OR 0 = 1, X = 1
Q5
A=0 B=1 C=1: (0 AND 1) = 0, 0 AND 1 = 0, X = 0 → The bracket result was combined with C using AND, but the expression uses OR. It should be 0 OR 1 = 1, so X = 1.
Q6
A=1 B=0 C=0: (1 AND 0) = 1, 1 OR 0 = 1, X = 1 → 1 AND 0 is 0, not 1, because AND needs both inputs to be 1. The correct working is 0 OR 0 = 0, so X = 0.
Section C: Definitions
Q1
X = (A AND B) OR C — Fill all 8 rows of A, B and C: work out the bracket (A AND B) in an extra column first, then combine it with C using OR to get output X.
Section D: Fill in the Blanks
Q1
X = (A AND B) OR C
Q2
X = (A AND B) OR C
Q3
Rows needed: 2 x 2 x 2 = 8
Q4
A=1, B=1, C=0: P = A AND B = 1 X = P OR C = 1
Q5
X = (A XOR B) AND NOT C
Section E: Spot the Error
Q1
B — Three inputs give 2^3 = 8 rows, not 6. Every combination of A, B and C must appear in the table.
Q2
C — AND gives 1 only when both inputs are 1. With A=1 and B=1, A AND B = 1, not 0.
Q3
C — OR gives 1 when at least one input is 1. With A=1 and B=0, A OR B = 1, not 0.
Q4
C — NOT reverses its input. With A=1, NOT A = 0, not 1. The intermediate values are then 0 and 0, so X = 0.
Q5
D — AND gives 1 only when both inputs are 1. Here the inputs are 0 and 1, so X = 0, not 1.