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Number System — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsNumber System3 Marks
Question
Find decimal equivalent of the octal number $(645)_8$.
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Answer

Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index portion.
The decimal equivalent of the octal number $(648)_8$ is
Given digits         $\begin{array}{lll}6 &\ 4 &\ 8\end{array}$
Position Number $\begin{array}{lll}2 &\ 1 &\ 0\end{array}$
Decimal value     $8^2 \quad 8^1 \quad 8^0$
$\begin{array}{ll}\text { Decimal Number } & 6 \times 8^2+4 \times 8^1+8 \times 8^0 \\ & =6 \times 64+4 \times 8+8 \times 1 \\ & =384+32+8 \\ & =424 \\ \text { Hence, } \quad(648)_8 & =(424)_{10}\end{array}$

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