To get an output value $ 1 $ from the given circuit, the input values of $ A $, $ B $, and $ C $ are:
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To solve digital logic circuits:
1. Identify the type of gates (AND, OR, NOT).
2. Write the Boolean expression for the output.
3. Substitute input values to determine the output.
\textbf{Step 1: Analyze the Circuit}
The given circuit consists of:
1. An AND gate with inputs $ A $ and $ B $.
2. An OR gate with inputs from the AND gate and $ C $.
The output $ Y $ is determined by the following logic:
$$
Y = (\text{AND}(A, B)) \, \text{OR} \, C
$$
This can be expressed as:
$$
Y = (A \cdot B) + C
$$
where:
$ \cdot $ represents the AND operation,
$ + $ represents the OR operation. Step 2: Determine Conditions for Output $ Y = 1 $
For $ Y = 1 $, either:
1. The AND gate output ($ A \cdot B $) must be $ 1 $, or
2. $ C = 1 $.
Case 1: AND Gate Output ($ A \cdot B = 1 $)
For $ A \cdot B = 1 $, both $ A $ and $ B $ must be $ 1 $:
$$
A = 1, \quad B = 1
$$
Case 2: $ C = 1 $
If $ C = 1 $, the OR gate will output $ 1 $ regardless of the AND gate's output.
\textbf{Step 3: Check Each Option}
Option (1): $ A = 0, B = 1, C = 0 $
$$
Y = (0 \cdot 1) + 0 = 0 + 0 = 0 \quad \text{(Incorrect)}
$$
Option (2): $ A = 0, B = 0, C = 1 $
$$
Y = (0 \cdot 0) + 1 = 0 + 1 = 1 \quad \text{(Correct, but not the only solution)}
$$
Option (3): $ A = 1, B = 0, C = 1 $
$$
Y = (1 \cdot 0) + 1 = 0 + 1 = 1 \quad \text{(Correct)}
$$
Option (4): $ A = 1, B = 0, C = 0 $
$$
Y = (1 \cdot 0) + 0 = 0 + 0 = 0 \quad \text{(Incorrect)}
$$
Step 4: Verify the Correct Option
From the analysis, Option (3) satisfies the condition $ Y = 1 $:
$$
A = 1, \quad B = 0, \quad C = 1
$$
