- 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.
|
83
|
82
|
81
|
80
|
8-1
|
8-2
|
|
1
|
0
|
6
|
7
|
0
|
0
|
|
or 10678
