Question

The representation of octal number \((532.2){_8}\) in decimal is ____ .

• A. \((346.25)_{10}\)
• B. \((532.864)_{10}\)
• C. \((340.67)_{10}\)
• D. \((531.668)_{10}\)

Hint:

Octal to Decimal Conversion. Multiply each octal digit by its place value (powers of 8). Integer part positions: ..., 8\(^2\), 8\(^1\), 8\(^0\). Fractional part positions: 8\(^{-1\), 8\(^{-2\), ... Sum the results.

Answer 1

The Correct Option is A

To convert an octal number (base 8) to decimal (base 10), we multiply each digit by the corresponding power of 8 based on its position relative to the radix point (octal point)
The octal number is (53(2)2)\(_8\)
Integer part: 532 Fractional part: 2 Decimal value = \( (5 \times 8^2) + (3 \times 8^1) + (2 \times 8^0) + (2 \times 8^{-1}) \) $$ = (5 \times 64) + (3 \times 8) + (2 \times 1) + (2 \times \frac{1}{8}) $$ $$ = 320 + 24 + 2 + \frac{2}{8} $$ $$ = 346 + \frac{1}{4} $$ $$ = 346 + 0
25 $$ $$ = 346
25 $$ So, (53(2)2)\(_8\) = (346
25)\(_{10}\)