Question 13 Marks
Find decimal equivalent of the octal number $(645)_8$.
Answer
View full question & 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 $8^2 \quad 8^1 \quad 8^0$
$\begin{array}{ll}\text { Decimal Number } & 6 \times 8^2+4 \times 8^1+8 \times 8^0 \\ & =6 \times 64+4 \times 8+8 \times 1 \\ & =384+32+8 \\ & =424 \\ \text { Hence, } \quad(648)_8 & =(424)_{10}\end{array}$
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 $8^2 \quad 8^1 \quad 8^0$
$\begin{array}{ll}\text { Decimal Number } & 6 \times 8^2+4 \times 8^1+8 \times 8^0 \\ & =6 \times 64+4 \times 8+8 \times 1 \\ & =384+32+8 \\ & =424 \\ \text { Hence, } \quad(648)_8 & =(424)_{10}\end{array}$