## Compliments

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:

• Compute the compliment of the SUBTRAHEND.

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:

1. (r-1)'s Compliment
2. r's Compliment

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).

legends (r-1)'s r's
Formula
Examples
Decimal Numbers
Octal Numbers