Question

What is the output of selective complement operation of 1010 and 1100?

• A. 1110
• B. 0110
• C. 0010
• D. 1010

Hint:

Selective Complement is performed using XOR. \[ A \oplus 0=A \] \[ A \oplus 1=\overline{A} \] Remember: XOR acts as a controlled complement operation.

Answer 1

The Correct Option is B

Concept:& nbsp;
Selective complement is a logic microoperation in which specific bits of a register are complemented according to another control word. This operation is performed using the XOR operation. Mathematically, \[ A \oplus B \] performs selective complementation because \[ 0 \oplus x = x \] and \[ 1 \oplus x = \overline{x}. \] Thus, whenever the control bit is \(1\), the corresponding bit of the data word is complemented.& nbsp;

Step 1: Write the given binary numbers.
Given: \[ 1010 \] and \[ 1100. \]& nbsp;

Step 2: Perform bit-by-bit XOR operation.
\[ \begin{array}{cccc} 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 \\ \hline 0 & 1 & 1 & 0 \end{array} \] Evaluating each bit: \[ 1\oplus1=0,\qquad 0\oplus1=1,\qquad 1\oplus0=1,\qquad 0\oplus0=0. \]& nbsp;

Step 3: Obtain the result.
Therefore, \[ 1010 \oplus 1100 = 0110. \]& nbsp;

Step 4: Conclusion.
The output of the selective complement operation is \[ \boxed{0110}. \]& nbsp;

Final Answer: \[ \boxed{0110} \] Hence, the correct option is \[ \boxed{\text{(B)}}. \]