Compliments are one of the most important aspects of arithmetic operations in digital systems. As we are pretty much familiar with the fact that SUBTRACTION is nothing but a COMPLIMENTED ADDITION, we can carry out a subtraction operation by using the following steps:
Compliment of any data is needed primarily to perform SUBTRACTION operations. The following example better clarifies the concept:
Suppose we have to calculate: a = (10 – 6)
We can do it via any of the two ways stated below:
In Digital Architecture Compliments are of following two types:
Since compliments are of two types, they are significantly different for different number systems. Consider the following table:
Basically in a number system, r represents RADIX or simply the BASE. Thus r’s compliment means to the compliment w.r.t. BASE, similarly (r-1)’s compliment means to the compliment w.r.t. (BASE-1).