Subjects number systems

Octal To Decimal

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Octal To Decimal


1. We are given the octal number $(206, 104)_8$ and need to convert it to decimal. 2. Recall that in base 8 (octal), each digit represents a power of 8. Positions to the left of the decimal point have positive powers, and to the right have negative powers. 3. Separate the number into integer part $206_8$ and fractional part $104_8$. 4. Convert integer part $206_8$ to decimal: $$206_8 = 2 \times 8^2 + 0 \times 8^1 + 6 \times 8^0 = 2 \times 64 + 0 + 6 = 128 + 6 = 134$$ 5. Convert fractional part $0.104_8$ to decimal: $$0.104_8 = 1 \times 8^{-1} + 0 \times 8^{-2} + 4 \times 8^{-3} = 1 \times \frac{1}{8} + 0 + 4 \times \frac{1}{512} = 0.125 + 0 + 0.0078125 = 0.1328125$$ 6. Combine integer and fractional parts: $$134 + 0.1328125 = 134.1328125$$ 7. Therefore, the decimal equivalent of $(206, 104)_8$ is $134.1328125$.