Explain the compliments used in digital system.

Complements are used in the digital system (computers) for logical manipulation and for the ease of subtraction operation. For a given base r there are two types of compliments.

1.  (r -1)’s compliment

For the give number N of n digits in base r system, the (r -1)’s compliment

is given by ( . Or we can consider as . Where m denotes the number of digits in fractional part of a real number and n is the no of digits in non fractional part. For an integer m=0. Eg. Decimal number system- 9’s compliment and binary number system-1’s compliment.

2.  (r ’s) compliment

For the give number N of n digits in base r system, the (r )’s compliment

is given by ( ). Eg. Decimal number system- 10’s compliment and binary number system-2’s compliment.

eg: for decimal number system:

 9’s compliment of 325.23 is  =1000-0.01-325.23 =674.76

10’s compliment of 325 is  =675

NOTE: We cannot calculate r’s compliment of floating numbers.