Decimal Number System
Decimal system is also called base-10 number system. It is a very basic number system,used throughout world for day-to-day use. It is learnt in schools before any mathematics and generally, known as only existing number system to layman.
- There are TEN symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
- These TEN symbols are known as DIGITS.
- Any number can be composed using these DIGITS.
Complementary numbers
For base-10 system, 9's complement and 10's complement of a number can be found.
10's complement:
The 10's complement of any decimal number is obtained by following formula
(10's complement of N) = 10^n - N
where, n = number of digits in N.
e.g. N = 1231.
so, n = 4 since N is four digit number.
(10's complement of 1231) = 10^4 - 1231
= 10000 - 1231
= 8769
9's complement:
The 9's complement of any decimal number is obtained by following formula
(9's complement of N) = 10^n - N - 1
= 10's complement - 1
or, simply put, (9's complement of N) = (n times 9) - N
where, n = number of digits in N.
e.g. N = 1231.
so, n = 4 since N is four digit number.
(9's complement of 1231) = 10^4 - 1231 - 1
= 10000 - 1231 - 1
= 8768
e.g N = 756
so, n = 3
(9's complement of 756) = (3 times 9) - 756
= 999 -756
= 243
The subtraction done in finding 9's complement of a number doesn't involve any borrow and hence is easy to calculate. The 10's complement is then obtained by just adding 1 to 9's complement.
0 1 2 3 4 5 6 7 8 9
