Question

Write the logic expression that matches the Truth Table below. A and C
are inputs, and Z is the output.
A
C Z
0
1 1
0
0 0
1
1 1
1
0
1

For , : Z = 0
For , : Z = 1
For , : Z = 1
For , : Z = 1

Answer 1

To write the logic expression that matches the given truth table with inputs \( A \) and \( C \) and output \( Z \), we first need to construct the truth table based on the information provided.

### Truth Table:

| A | C | Z |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

### Analyzing the Table:

From the truth table, we can summarize when \( Z \) is 1:
- \( Z = 1 \) for \( (A = 0, C = 1) \)
- \( Z = 1 \) for \( (A = 1, C = 0) \)
- \( Z = 1 \) for \( (A = 1, C = 1) \)

### Logical Expression:

We can create the logical expression for \( Z \) based on these observations:
1. The first condition \( A = 0 \) and \( C = 1 \) can be expressed as \( \overline{A}C \).
2. The second condition \( A = 1 \) and \( C = 0 \) can be expressed as \( A\overline{C} \).
3. The third condition \( A = 1 \) and \( C = 1 \) can be expressed as \( AB \).

Combining these conditions with the OR operation, we get the final logical expression for \( Z \):

\[
Z = \overline{A}C + A\overline{C} + AC
\]

### Simplifying:

The expression can be simplified as follows:
- The term \( A\overline{C} + AC \) simplifies to \( A \) since it covers both scenarios when \( A = 1 \).

So the simplified expression would be:
\[
Z = \overline{A}C + A
\]

### Final Answer:

Thus, the final logic expression that matches the given truth table is:

\[
Z = A + \overline{A}C
\]