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.
- Add it with the MENUEND to get the difference.
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:
- (r-1)'s Compliment
- 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 |  |
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| Examples | ||
| Decimal Numbers |  |
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| Octal Numbers |  |
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| Hexadecimal Numbers |  |
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| Decimal Numbers |  |
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