Question

The result of $101_2 \times 10_2$ is _ _ _ _ .

• A. $1010_2$
• B. $1000_2$
• C. $1110_2$
• D. $1100_2$

Hint:

Multiplying a binary number by: \[ 10_2 \] simply shifts the number one bit to the left. Similarly, \[ 100_2 \] shifts by two positions and \[ 1000_2 \] shifts by three positions.

Answer 1

The Correct Option is A

Concept: Binary multiplication follows the same principles as decimal multiplication, except that only two digits are available: \[ 0 \quad \text{and} \quad 1 \] The basic multiplication rules are: \[ 0 \times 0 = 0 \] \[ 0 \times 1 = 0 \] \[ 1 \times 0 = 0 \] \[ 1 \times 1 = 1 \]

Step 1: Perform binary multiplication directly. Given: \[ 101_2 \times 10_2 \] Since \[ 10_2 = 2_{10} \] multiplying by \(10_2\) is equivalent to shifting the number one position to the left. \[ 101_2 \rightarrow 1010_2 \] Thus, \[ 101_2 \times 10_2 = 1010_2 \]

Step 2: Verification using decimal conversion. Convert \(101_2\) to decimal: \[ 101_2 = 1(2^2)+0(2^1)+1(2^0) \] \[ =4+0+1 \] \[ =5_{10} \] Convert \(10_2\) to decimal: \[ 10_2 = 2_{10} \] Multiply: \[ 5\times2=10 \] Convert \(10_{10}\) back to binary: \[ 10_{10}=1010_2 \] The answer is verified. Hence, \[ \boxed{1010_2} \]