Question

Division of \( 111000_{(2)} \) by \( 100_{(2)} \) in binary is ______.

• A. \( 111_{(2)} \)
• B. \( 1110_{(2)} \)
• C. \( 1100_{(2)} \)
• D. \( 1001_{(2)} \)

Hint:

To perform binary division, follow the same steps as in decimal division, but use binary subtraction (i.e., 1 - 1 = 0, 1 - 0 = 1). Carry down the next digit from the dividend at each step.

Answer 1

The Correct Option is C

To divide \( 111000_{(2)} \) by \( 100_{(2)} \), we follow the binary long division process: 1. First step: Divide the first three bits of \( 111000_{(2)} \), which is \( 111 \), by \( 100 \). \[ 111 \div 100 = 1 \quad \text{(remainder 011)} \] 2. Second step: Bring down the next bit, which is \( 0 \), making the remainder \( 110 \). \[ 110 \div 100 = 1 \quad \text{(remainder 010)} \] 3. Third step: Bring down the final bit, which is \( 0 \), making the remainder \( 100 \). \[ 100 \div 100 = 1 \quad \text{(remainder 000)} \] So, the quotient is \( 1100_{(2)} \), and the remainder is \( 000_{(2)} \). Conclusion: The result of the division is \( 1100_{(2)} \), so the correct answer is (3) \( 1100_{(2)} \).