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Convert octal 623.77 to decimal, binary, hex

Short answer

To decimal: 6×8²+2×8+3+7/8+7/64 = 403.984375. To binary: each octal digit to 3 bits gives 110 010 011.111 111. To hexadecimal: regroup binary in 4s from the point → (193.FC)₁₆.

Convert Octal (623.77) to decimal, binary and hexadecimal.

To decimal

(623.77)8=6×82+2×8+3+7×8−1+7×8−2=384+16+3+0.875+0.109375=403.984375\begin{aligned} (623.77)_8 &= 6\times8^2 + 2\times8 + 3 + 7\times8^{-1} + 7\times8^{-2} \\ &= 384 + 16 + 3 + 0.875 + 0.109375 \\ &= 403.984375 \end{aligned}

Decimal: (403.984375)10(403.984375)_{10}

To binary

Replace each octal digit by 3 bits: 6 = 110, 2 = 010, 3 = 011, 7 = 111, 7 = 111.

Binary: (110010011.111111)2(110010011.111111)_2

To hexadecimal

Regroup the binary into 4 bits from the point:

 Integer : 0001 1001 0011  -> 1 9 3
 Fraction: 1111 1100       -> F C

Hexadecimal: (193.FC)16(193.FC)_{16} (check: 403+252/256=403.984375403 + 252/256 = 403.984375)

✓ Answer checked by Claude Opus 5.5 (high effort)

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