Hex to Octal

Hexadecimal (Hex) Number:Hexadecimal is a base-sixteen numeral system that uses sixteen symbols: 0-9 and A-F, where A represents 10, B represents 11, and so on up to F representing 15. It's commonly used in computing for representing binary-coded values in a more compact form.

Hexadecimal Number Example:An example of a hexadecimal number is 2F8A. Each digit in a hexadecimal number represents a power of 16, with the rightmost digit representing 16^0, the next representing 16^1, 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: Hexadecimal to Octal

1. Convert Hexadecimal to Binary: Convert each hexadecimal digit to its binary equivalent.
2. Group Binary Digits in Sets of Three: Group the binary digits obtained in step 1 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.
3. Convert Each Group to Octal: Convert each three-digit binary group to its octal equivalent.
4. Combine Octal Digits: Combine the octal digits obtained from each group to form the final octal number.

Example: Convert Hexadecimal 2F8A to Octal

Hexadecimal Number: 2F8A

1. Convert Hexadecimal to Binary:
   2 (0010 in binary)
   F (1111 in binary)
   8 (1000 in binary)
   A (1010 in binary)

2. Group Binary Digits in Sets of Three:
   001 011 111 100 010

3. Convert Each Group to Octal:
   001 (1 in octal)
   011 (3 in octal)
   111 (7 in octal)
   100 (4 in octal)
   010 (2 in octal)

4. Combine Octal Digits:
   131742

Therefore, the octal representation of the hexadecimal number 2F8A is 131742.