Octal toDecimal

Octal Number:An octal number is a base-eight numeral system that uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. 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.

Octal Number Example:An example of an octal number is 345. Here, 3 is in the 512s place (8^2), 4 is in the 64s place (8^1), and 5 is in the 8s place (8^0).

Decimal Number:A decimal number is a base-ten numeral system that uses ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It's the numeral system most commonly used by people in everyday life.

Decimal Number Example:An example of a decimal number is 456. Here, 4 is in the hundreds place (10^2), 5 is in the tens place (10^1), and 6 is in the ones place (10^0).

Conversion Process: Octal to Decimal

1. Write the Octal Number: Start with the given octal number.
2. Assign Powers of 8: Assign powers of 8 to each digit from right to left, starting with 8^0 for the rightmost digit.
3. Multiply and Sum: Multiply each octal digit by its corresponding power of 8 and sum all these products to get the decimal equivalent.

Example: Convert Octal 345 to Decimal

Octal Number: 345

Assign Powers of 8:
5 * 8^0 (1) = 5
4 * 8^1 (8) = 32
3 * 8^2 (64) = 192

Multiply and Sum:
5 + 32 + 192 = 229

Therefore, the decimal representation of the octal number 345 is 229.