Octal to Binary

Octal to Binary Converter


An Octal to Binary Converter is a free online tool used to convert numbers from the octal numeral system to the binary numeral system. Let's break down these two numeral systems:

  • Octal Numeral System:
    • Base: Octal is a base-8 numeral system, which means it uses eight distinct digits to represent numbers: 0, 1, 2, 3, 4, 5, 6, and 7. Example: In octal, the number 17 is represented as 21, because it's 2 times 8 to the power of 1 plus 1 times 8 to the power of 0 (28^1 + 18^0 = 16 + 1 = 17).
  • Binary Numeral System:
    • Base: Binary is a base-2 numeral system, which means it uses only two distinct digits to represent numbers: 0 and 1. Example: In binary, the number 17 is represented as 10001, because it's 1 times 2 to the power of 4 plus 0 times 2 to the power of 3 plus 0 times 2 to the power of 2 plus 0 times 2 to the power of 1 plus 1 times 2 to the power of 0 (12^4 + 02^3 + 02^2 + 02^1 + 1*2^0 = 16 + 0 + 0 + 0 + 1 = 17).

To convert an octal number to binary, you can follow these steps:

  • Replace each octal digit with its equivalent binary representation. Use the following mapping:
    • Octal 0 = Binary 000
    • Octal 1 = Binary 001
    • Octal 2 = Binary 010
    • Octal 3 = Binary 011
    • Octal 4 = Binary 100
    • Octal 5 = Binary 101
    • Octal 6 = Binary 110
    • Octal 7 = Binary 111
  • Concatenate the binary representations of each octal digit to form the binary representation of the entire octal number.

For example, to convert the octal number 21 to binary:

  • Replace 2 with 010 (Octal 2 is equivalent to Binary 010).
  • Replace 1 with 001 (Octal 1 is equivalent to Binary 001).
  • Concatenate them: 010 001.

So, the octal number 21 is equivalent to the binary number 010001.

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