Question

The decimal equivalent of ${\left(264\right)}_8$ is

• A. $180$
• B. $170$
• C. $166$
• D. None of these

Answer 1

The correct option is A

$180$

Explanation for the correct option:

To find the decimal equivalent of ${\left(264\right)}_8$

Given octal number is $264$

To find the equivalent decimal number, mutiply each number of the octal number by $8^n$, where $n$ is the corresponding place value of the octal number and then, sum all the terms. Hence,

$$\begin{gathered} =8^2\left(2\right)+8^1\left(6\right)+8^0\left(4\right) \\ =64\left(2\right)+8\left(6\right)+4 \\ =128+48+4 \\ =180 \end{gathered}$$

Hence the decimal equivalent of ${\left(264\right)}_8$ is $180$.

Therefore, option (A) is the correct answer.