Question

Addition of two binary numbers 11 and 01 gives the binary number

• A. 12
• B. 101
• C. 10
• D. 100

Hint:

To verify any binary operation quickly, convert the binary numbers to their decimal equivalents, perform the operation, and convert the result back to binary.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Binary addition is the process of summing numbers using base-2 rules.
Key Formula or Approach:
The fundamental addition rules for binary digits are:
\[ 0 + 0 = 0 \]
\[ 0 + 1 = 1 \]
\[ 1 + 0 = 1 \]
\[ 1 + 1 = 10 \text{ (which is 0 with a carry of 1)} \]
\[ 1 + 1 + 1 \text{ (carry)} = 11 \text{ (which is 1 with a carry of 1)} \]

Step 2: Detailed Explanation:
Let us align and add the two binary numbers $11_2$ and $01_2$:
\[ \begin{array}{r@{\quad}l} 11 & \text{(Carry row)} \phantom{+} 11 & \text{(Binary 11)} + \phantom{0}01 & \text{(Binary 01)} \hline 100 & \text{(Sum)} \end{array} \]
Step-by-step digit sum:
1. Rightmost column: $1 + 1 = 10$ (write 0, carry 1 to the next left column).
2. Leftmost column: $1 (\text{original}) + 0 (\text{original}) + 1 (\text{carry}) = 10$ (write 0, carry 1).
3. Final carry of 1 is placed in the third position to the left.
This results in $100_2$.
Verification in decimal:
$11_2 = 3_{10}$
$01_2 = 1_{10}$
Sum: $3 + 1 = 4_{10}$, and $4_{10} = 100_2$.
The result is correct.

Step 3: Final Answer
The correct option is (D).