How to convert octal to binary

The octal number system is a base-8 number system. This means that it has a total of 8 symbols, $0, 1, 2, 3, 4, 5, 6, 7$, for representing the values.

In computers, octal numbers are represented in two ways:

• Writing $8$ as the suffix of the value (e.g. $305_8$.).
• Writing 0o as the prefix of the value(e.g.0o$305$)

The binary number system, on the other hand, is a base-2 number system. This means that it has a total of 2 symbols,$ 0$ and $1$, for representing the values.

In computers, binary numbers are represented in the following two ways:

• Writing $2$ as the suffix of the value (e.g. $10110_2$).
• Writing 0b as the prefix of the value (e.g. 0b$10110$)

Converting a number from Octal to Binary

The following steps are needed to convert from Octal to Binary:

• Convert each octal digit to its 3-digit binary representation. Each of the digits must be treated as a decimal value.
• Combine these binary representations to form a single binary number.

Example

If we have an Octal value of $305$₈, its binary representation would be:

= 305₈

= (011 000 101)₂

= (011000101)₂

Hence, we can form the following table for octal to binary conversion, where each digit is represented with its corresponding binary representation.