Question

Which of the following is an octal number equal to decimal number \((896)_{10}\)?

• A. \( 0061 \)
• B. \( 6001 \)
• C. \( 1006 \)
• D. \( 1600 \)

Hint:

To convert a decimal number to any base \(b\), repeatedly divide the number by \(b\) and collect the remainders in reverse order. To verify, convert the octal number back to decimal: \( (1600)_8 = 1 \times 8^3 + 6 \times 8^2 + 0 \times 8^1 + 0 \times 8^0 = 1 \times 512 + 6 \times 64 + 0 + 0 = 512 + 384 = 896_{10} \).

Answer 1

The Correct Option is D

Step 1: To convert a decimal number to octal (base-8), we use the method of successive division by 8. We divide the decimal number by 8 repeatedly and record the remainders until the quotient becomes 0.

Step 2: Read the remainders from bottom to top to get the octal representation. The remainders are 1, 6, 0, 0.

Step 3: Therefore, the octal equivalent of the decimal number \( (896)_{10} \) is \( (1600)_8 \).

Step 4: Comparing this result with the given options, option (d) matches.