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:
The logic circuit shows two inputs \(A\) and \(B\).
Input \(A\) passes through a NOT gate (inverter), producing \(\bar{A}\).
Then, \(\bar{A}\) and \(B\) serve as inputs to an AND gate (indicated by a straight back and curved front shape in standard logic gate diagrams, and verified by standard digital logic context given the options). Step 2: Key Formula or Approach:
The boolean expression for the circuit is \(Y = \bar{A} \cdot B\).
We perform a bitwise NOT operation on \(A\), followed by a bitwise AND operation with \(B\). Step 3: Detailed Explanation:
Given inputs:
\(A = 1101\)
\(B = 1010\)
First, pass \(A\) through the NOT gate to get \(\bar{A}\):
\(\bar{A} = \text{NOT}(1101) = 0010\)
Next, feed \(\bar{A}\) and \(B\) into the AND gate:
\(Y = \bar{A} \text{ AND } B\)
\(Y = 0010 \text{ AND } 1010\)
Perform bitwise AND (1 AND 1 = 1, otherwise 0):
Bit 3: 0 AND 1 = 0
Bit 2: 0 AND 0 = 0
Bit 1: 1 AND 1 = 1
Bit 0: 0 AND 0 = 0
Resulting binary output:
\(Y = 0010\) Step 4: Final Answer:
The output sequence \(Y\) is \(0010\).
