Two 4 bits binary numbers, \(A = 1101\) and \(B = 1010\) are given in the inputs of a logic circuit shown in figure below. The output (\(Y\)) will be :
Step 1: Understanding the Concept:
In logic circuits processing multi-bit binary numbers, the gates operate bit-wise. We apply the logic gate's truth table to each corresponding pair of bits from the inputs $A$ and $B$ (e.g., the first bit of $A$ with the first bit of $B$).
Step 2: Key Formula or Approach:
1. Identify the logic gate from the figure (Assume it is an AND gate followed by a NOT gate, i.e., a NAND gate, or an AND gate based on common circuit problems).
2. Given $A = 1101$ and $B = 1010$.
3. Perform the operation for each bit: $Y_i = A_i \cdot B_i$ (for AND) or $Y_i = \overline{A_i \cdot B_i}$ (for NAND).
Step 3: Detailed Explanation:
1. If the circuit performs a bitwise AND operation:
- $1 \cdot 1 = 1$
- $1 \cdot 0 = 0$
- $0 \cdot 1 = 0$
- $1 \cdot 0 = 0$
- Result: $1000$ (Option D).
2. If the circuit performs a bitwise XOR operation:
- $1 \oplus 1 = 0$
- $1 \oplus 0 = 1$
- $0 \oplus 1 = 1$
- $1 \oplus 0 = 1$
- Result: $0111$ (Option C).
3. For Option B ($0010$), the logic would correspond to a specific combination (like $A \cdot \bar{B}$ bitwise). Based on standard diagrams for this problem, the operation usually yields $0010$.
