Octal to Decimal Conversion -
Decimal to Octal Conversion

Convert octal numbers to decimal numbers and vice versa

Octal and Decimal

Octal and decimal numbers are both numbering systems that we use to represent numbers, but they differ in their base or radix.

Decimal system

The decimal system is what we use most in daily life. It is a base 10 system, which means there are ten digits (0 through 9) to represent numbers. When we count in the decimal system and we reach the number 9, we go back to 0 and add 1 to the next digit to the left, starting with a new position if necessary.

Octal system

The octal system, on the other hand, is a base 8 system. This means it only has eight digits (0 through 7) to represent numbers. When we count in the octal system and we reach the number 7, we go back to 0 and add 1 to the next digit to the left, starting with a new position if necessary.

The conversion between these two systems is relatively simple. For the conversion from decimal to octal, you start with the decimal number and divide it by 8, the remainder is the least significant digit (right) in the octal equivalent. You repeat this process with the quotient until the quotient is zero. The remaining remainders form the octal equivalent, but in reverse order.

For the conversion from octal to decimal, you multiply each digit in the octal number by 8 to the power of its position, starting at 0 from the right. The decimal equivalent is the sum of these products.

Example:

Octal to Decimal: Octal 20 = 2*(8^1) + 0*(8^0) = 16 in Decimal

Decimal to Octal: Decimal 18 = 2*(8^1) + 2*(8^0) = 22 in Octal