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

…..

Answer 1

To derive a logic expression from the Truth Table, we first need to clarify the format of the table and how the inputs \( A \) and \( C \) correlate to the outputs \( Z \). Based on the provided information, I will assume the following format:

Here is the presumed truth table based on your description (inputs A and C, with the output Z given):

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

From this table, we can see the following true cases for output \( Z \):
- \( (A=0, C=1) \) → \( Z=1 \)
- \( (A=1, C=1) \) → \( Z=1 \)

Now we can create the logic expression based on these outputs. The expression is formed by analyzing the rows where \( Z \) is true (1).

1. For \( (A=0, C=1) \):
- This can be represented as \( \overline{A} C \).
2. For \( (A=1, C=1) \):
- This can be represented as \( A C \).

Combining these, the final logic expression for \( Z \) is as follows:

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

This can be further simplified:

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

Since \( \overline{A} + A \) is always true (1 for any value of \( A \)), the expression simplifies to:

\[
Z = C
\]

So the final expression is:
\[
Z = C
\]

This indicates that the output \( Z \) depends solely on the input \( C \).