Binary to Octal

Binary Number:A binary number is a numeral system based on base-two, using only two digits: 0 and 1. It's commonly used in computing and digital electronics.

Binary Number Example:An example of a binary number is 110101. Each digit represents a power of 2, with the rightmost digit representing 2^0, the next representing 2^1, and so on.

Octal Number:Octal is a base-eight numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. It's less common in modern computing but was historically used due to its ease of conversion with binary numbers.

Octal Number Example:An example of an octal number is 645. Each digit in an octal number represents a power of 8, with the rightmost digit representing 8^0, the next representing 8^1, and so on.

Conversion Process: Binary to Octal

1. Group Binary Digits in Sets of Three: Start by grouping the binary digits in sets of three from right to left. If the last group has fewer than three digits, add zeros to the left to make it three digits.
2. Convert Each Group to Octal: Convert each three-digit binary group to its octal equivalent.
3. Combine Octal Digits: Combine the octal digits obtained from each group to form the final octal number.

Example: Convert Binary 110110101 to Octal

Binary Number: 110110101

Group in Sets of Three:
110 110 101

Convert Each Group to Octal:
110 (6 in octal)
110 (6 in octal)
101 (5 in octal)

Combine Octal Digits:
666

Therefore, the octal representation of the binary number 110110101 is 666.