Question

Binary multiplication of \(1100\) and \(1011\):

• A. \(10000100\)
• B. \(10000110\)
• C. \(10001000\)
• D. \(11111100\)

Hint:

A quick method is to convert binary numbers into decimal, multiply them, and convert the result back to binary for verification.

Answer 1

The Correct Option is A

Step 1: Convert each binary number to decimal.
$1100_2 = 8+4 = 12$ and $1011_2 = 8+2+1 = 11$. Working in decimal first gives us a quick way to check the binary answer.
Step 2: Multiply in decimal.
$12 \times 11 = 132$.
Step 3: Break 132 into powers of two.
$132 = 128 + 4 = 2^{7} + 2^{2}$.
Step 4: Write the binary form.
Powers $7$ and $2$ are set, all others clear, giving $10000100_2$.
Step 5: Cross-check by binary long multiplication.
Adding the shifted partial products $1100 + 11000 + 1100000$ also yields $10000100_2$, matching Step 4.
Step 6: Match the option.
The product is $10000100$.
\[ \boxed{10000100} \]