Completing a truth table from an expression: one gate
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. X = A AND B. Row: A = 1, B = 0. What goes in column X?
2. X = A AND B. Which row gives X = 1?
3. X = NOT A. Row: A = 0. What goes in column X?
4. To complete the truth table for X = NOT A, how many inputs do you apply the rule to in each row?
5. X = A XOR B. Row: A = 1, B = 1. What goes in column X?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1X = A AND B | AAND gives 1 when both inputs are 1, so this row should have X = 1, not 0 | |
| 2X = A XOR B | BIn each row, write 1 in column X only when A and B are both 1; otherwise write 0 | |
| 3For a one-input expression, flip the value of A in every row and write it in column X, so A = 0 gives X = 1 | CX = NOT A | |
| 4For the row where A = 1 and B = 1, this expression gives an output of 1 because both inputs are 1 | DXOR gives 0 when both inputs are the same, so this row should have X = 0, not 1 | |
| 5A = 1, B = 1 gives X = 0 for X = A AND B | EX = A AND B | |
| 6A = 1, B = 1 gives X = 1 for X = A XOR B | FIn each row, write 1 in column X only when A and B are different; write 0 when they are the same |
C
Definitions
X = A AND B
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
X = A ___ B
2.
X = ___ A
3.
X = A ___ B
4.
X = A AND B
A = 1, B = 0
X = _
5.
X = A XOR B
A = 1, B = 1
X = _
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
X = A AND B
B
0 0 1
C
0 1 0
D
1 1 1
Question 2
A
X = NOT A
B
A X
C
0 1
D
1 1
Question 3
A
X = A XOR B
B
A B X
C
0 1 0
D
1 1 0
Question 4
A
X = A OR B
B
0 0 0
C
1 0 1
D
1 1 0
Question 5
A
X = A XOR B
B
0 0 1
C
0 1 1
D
1 0 1
E
1 1 0
Answer Key
Completing a truth table from an expression: one gate
Section A: Quick Questions
Q1
A — X = 0
Q2
B — A = 1, B = 1
Q3
A — X = 1
Q4
A — One input: A
Q5
B — X = 0
Section B: Match the Pairs
Q1
X = A AND B → In each row, write 1 in column X only when A and B are both 1; otherwise write 0
Q2
X = A XOR B → In each row, write 1 in column X only when A and B are different; write 0 when they are the same
Q3
For a one-input expression, flip the value of A in every row and write it in column X, so A = 0 gives X = 1 → X = NOT A
Q4
For the row where A = 1 and B = 1, this expression gives an output of 1 because both inputs are 1 → X = A AND B
Q5
A = 1, B = 1 gives X = 0 for X = A AND B → AND gives 1 when both inputs are 1, so this row should have X = 1, not 0
Q6
A = 1, B = 1 gives X = 1 for X = A XOR B → XOR gives 0 when both inputs are the same, so this row should have X = 0, not 1
Section C: Definitions
Q1
X = A AND B — Complete the truth table row by row: apply the gate rule to the input values A and B in each row and write the result in column X. AND gives 1 only when both inputs are 1.Section D: Fill in the Blanks
Q1
X = A AND BQ2
X = NOT AQ3
X = A XOR BQ4
X = A AND B
A = 1, B = 0
X = 0Q5
X = A XOR B
A = 1, B = 1
X = 0Section E: Spot the Error
Q1
B — AND gives 1 only when both inputs are 1. With A = 0 and B = 0 the output X must be 0, so the row should be 0 0 0.
Q2
D — NOT reverses the input. When A = 1, X = NOT A is 0, so the row should be 1 0.
Q3
C — XOR gives 1 when the inputs are different. A = 0 and B = 1 are different, so X should be 1 and the row should be 0 1 1.
Q4
A — The row 1 1 0 shows the output is 0 when both inputs are 1. That is XOR behaviour, so the expression should be X = A XOR B.
Q5
B — XOR gives 0 when both inputs are the same. With A = 0 and B = 0, X should be 0, so the row should be 0 0 0.