Discussion
What is the OCTAL equivalent of the HEXADECIMAL number \((ADF)_{16}\) ?
Answer: D
The octal equivalent is \((5337)_{8}\).
Convert through binary: each hexadecimal digit becomes four bits, then regroup into threes from the right for octal.
\[ \begin{aligned} A\,D\,F &= 1010\ 1101\ 1111 \\ &= 101\ 011\ 011\ 111 \\ &= 5\ 3\ 3\ 7 \end{aligned} \]
Check in decimal: \(ADF_{16} = 10 \times 256 + 13 \times 16 + 15 = 2783\), and \(5 \times 512 + 3 \times 64 + 3 \times 8 + 7 = 2783\). The other options differ by a digit and fail this check.
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