Question

convert 537 octal to decimal​

Answer 1

$\texttt{\textsf{\large{\underline{Answer}:}}}$

• (537)₈ = (351)₁₀

$\texttt{\textsf{\large{\underline{Solution}:}}}$

Given number: (537)₈

The decimal equivalent of the number will be:

= (5 × 8²) + (3 × 8¹) + (7 × 8⁰)

= (5  × 64) + (3 × 8) + (7 × 1)

= 320 + 24 + 7

= (351)₁₀

Therefore:

> (537)₈ = (351)₁₀

$\texttt{\textsf{\large{\underline{Steps}:}}}$

• Multiply each octal digit from the last with the successive powers of 8 (starting with 0) and add them up.
• Result obtained will be the decimal equivalent of the octal number.

Answer 2

$\textbf{\large Question}$

    $\textsf{ (537)_8 \rightarrow (?)_{10} }$

$\textbf{\large Answer}$

    $\textsf{While converting from a number system other than decimal to decimal number}\\\textsf{system can be obtained by adding the product of source base raised to the}\\\textsf{successive powers from 0 and the digits.}$

    $\text{Given, }$

        $\textsf{ (537)_8 \rightarrow (?)_{10} }$

            $\textsf{} = (5 \: \cdot \: 8^2) + (3 \: \cdot \: 8^1) + (7 \: \cdot \: 8^0) \\ = (5 \: \cdot \: 64) + (3 \: \cdot \: 8) + (7 \: \cdot \: 1) \\ = (320) + (24) + (7) \\ = 351$

     $\textsf{ \therefore \: (537)_8 \rightarrow (351)_{10} }$

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