Octal

After understanding how the decimal number system works, it is quite easy to learn other bases, such as base 8 (octal). They all work basically the same way. In base 8, the available digits are 0 through 7, and each number occupies a place value. The place values are:

We can designate that a number is in a base other than base 10 (decimal) by using subscripts. Note: If there is no subscript, the number is assumed to be decimal. Let's use the number 123.6 in base 8 - it must be written as 123.68.

The number 123.68 can be converted to a decimal as:

1 * 82 + 2 * 81 + 3 * 80 + 6 * 8-1

1 * 64 + 2 * 8 + 3 * 1 + 6 * (1 / 8)

83.75

Now, using the number 567, we'll show how to convert it from the decimal system to the octal system. Start by looking for the largest power of 8 less than 567. This would be 512 or 83. So in the 83 place value, we put a 1. That leaves us with a remainder of 55. The next place value is 82, but 64 is greater than 55 so that place holds a zero. The next place value is 81. 55 divided by 8 gives 6 for the 81 place value, with a remainder of 7 left over for the next column. The leftover gets placed in the ones column.

or 1067₈