Question:
Binary multiplication of \(1100\) and \(1011\):
Binary multiplication of \(1100\) and \(1011\):
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A quick method is to convert binary numbers into decimal, multiply them, and convert the result back to binary for verification.
Updated On: Jun 11, 2026
- \(10000100\)
- \(10000110\)
- \(10001000\)
- \(11111100\)
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The Correct Option is A
Solution and Explanation
Concept:
Binary multiplication follows the same procedure as decimal multiplication.
First convert to decimal for verification.
\[
1100_2 = 12_{10}
\]
\[
1011_2 = 11_{10}
\]
Step 1: Multiply in decimal form.
\[ 12\times11=132 \]
Step 2: Convert 132 to binary.
\[ 132=128+4 \] \[ 132 = 10000100_2 \]
Step 3: Verify using binary multiplication.
\[ 1100 \times 1011 \] \[ = 1100 +11000 +00000 +1100000 \] \[ = 10000100 \] Therefore, \[ \boxed{10000100} \] \[ \boxed{\text{Answer (A)}} \]
Step 1: Multiply in decimal form.
\[ 12\times11=132 \]
Step 2: Convert 132 to binary.
\[ 132=128+4 \] \[ 132 = 10000100_2 \]
Step 3: Verify using binary multiplication.
\[ 1100 \times 1011 \] \[ = 1100 +11000 +00000 +1100000 \] \[ = 10000100 \] Therefore, \[ \boxed{10000100} \] \[ \boxed{\text{Answer (A)}} \]
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