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


Would A + C work

Answer 1

To determine the logic expression that matches the provided truth table, we first need to clarify the values for A, C, and Z. Based on the format you've provided, it appears that the truth table might have been misformatted. It seems that some combinations of inputs are missing or misaligned with their respective outputs.

Let's represent the information you've provided in a more standard truth table format.

Assuming that the pairs of inputs and their corresponding outputs are structured as follows:

\[
\begin{array}{|c|c|c|}
\hline
A & C & Z \\
\hline
0 & 0 & 0 \\
0 & 1 & 1 \\
1 & 0 & 0 \\
1 & 1 & 1 \\
\hline
\end{array}
\]

From this table, we can summarize the output Z based on the inputs A and C:

- For \(A = 0\), \(C = 0\): Z = 0
- For \(A = 0\), \(C = 1\): Z = 1
- For \(A = 1\), \(C = 0\): Z = 0
- For \(A = 1\), \(C = 1\): Z = 1

Now we can express the output Z as a function of inputs A and C.

We see that Z is 1 when:

- \(A = 0\) and \(C = 1\) (first row)
- \(A = 1\) and \(C = 1\) (fourth row)

This can be written in logical expression form as:

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

Alternatively, we can factor the expression:

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

This means Z is true (1) whenever C is true (1), regardless of A. Therefore, the correct expression that matches this truth table is:

\[ Z = C \]

To answer your initial question, the expression \( A + C \) would not work as it would yield 1 if either A or C is 1, which does not match the desired output mappings from your truth table.

Answer 2

Xo