Question

The correct result of 2's complement addition operation for the following values is ______. \[ 0010 \quad (+2) \] \[ 0011 \quad (+3) \]

• A. 0101
• B. 0100
• C. 1100
• D. 1110

Hint:

Important Binary Values: \[ 2=(0010)_2 \] \[ 3=(0011)_2 \] \[ 5=(0101)_2 \] For positive numbers, 2's complement addition is identical to ordinary binary addition.

Answer 1

The Correct Option is A

Concept: In 2's complement arithmetic, positive numbers are represented in their ordinary binary form. The given numbers are: \[ +2=(0010)_2 \] \[ +3=(0011)_2 \] Since both numbers are positive, ordinary binary addition is performed.

Step 1: Write the numbers vertically.
\[ \begin{array}{cccc} 0& 0& 1& 0 +& 0& 0& 1& 1 \hline \end{array} \]

Step 2: Add from right to left.
\[ 0+1=1 \] \[ 1+1=10 \] Write 0 and carry 1. \[ 0+0+1=1 \] \[ 0+0=0 \]

Step 3: Obtain the final binary result.
\[ 0010 \] \[ +0011 \] \[ =0101 \]

Step 4: Verify using decimal conversion.
\[ 2+3=5 \] Binary representation of 5 is: \[ 5=(0101)_2 \] Thus the result is correct. \[ \boxed{0101} \] Hence option (A) is correct.