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How to convert octal to binary

Educative Answers Team

The octal number system is a base-8 number system. This means that it has a total of 8 symbols, 0,1,2,3,4,5,6,70, 1, 2, 3, 4, 5, 6, 7, for representing the values.

In computers, octal numbers are represented in two ways:

  • Writing 88 as the suffix of the value (e.g. 3058305_8.).
  • Writing 0o as the prefix of the value(e.g.0o305305)

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 11, for representing the values.

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

  • Writing 22 as the suffix of the value (e.g. 10110210110_2).
  • Writing 0b as the prefix of the value (e.g. 0b1011010110)

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.
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Example

If we have an Octal value of 3053058, 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.

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