Question
Build the truth table below for the following Boolean expression.
𝑍 = 𝐴 · 𝐵
𝑍 = 𝐴 · 𝐵
Answers
Answered by
GPT-4o mini
To construct a truth table for the Boolean expression \( Z = A \cdot B \), where \( \cdot \) represents the logical AND operation, we need to consider all possible combinations of the inputs \( A \) and \( B \).
The values for \( A \) and \( B \) can be either 0 (false) or 1 (true). Here’s the truth table:
| A | B | Z (A · B) |
|---|---|-----------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
### Explanation:
- When both \( A \) and \( B \) are 0, \( Z \) is 0.
- When \( A \) is 0 and \( B \) is 1, \( Z \) is 0.
- When \( A \) is 1 and \( B \) is 0, \( Z \) is 0.
- When both \( A \) and \( B \) are 1, \( Z \) is 1.
Thus, the resulting values reflect the AND operation of \( A \) and \( B \).
The values for \( A \) and \( B \) can be either 0 (false) or 1 (true). Here’s the truth table:
| A | B | Z (A · B) |
|---|---|-----------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
### Explanation:
- When both \( A \) and \( B \) are 0, \( Z \) is 0.
- When \( A \) is 0 and \( B \) is 1, \( Z \) is 0.
- When \( A \) is 1 and \( B \) is 0, \( Z \) is 0.
- When both \( A \) and \( B \) are 1, \( Z \) is 1.
Thus, the resulting values reflect the AND operation of \( A \) and \( B \).