# SUBTRACTION IN COMPUTERS

HOW DO COMPUTERS SUBTRACT IN ANY EQUATION?

Computer is one of the best inventions in the whole world. Now in the era of electronics, computers are shrinking in the size.  The dream of having pocket computers which was shown in many Hollywood as well as many film industry is now a reality.

Many unimaginable discoveries and inventions are done with the help of computers. As in this age the  of semiconductors and embedded systems we are achieving what was a dream, about 60-70 years ago.

Now to achieve such a dream, the hard-work and dedication needed was given by many scientists whose aim was to uplift the society.  Now if we want to invent something we need good hold on arithmetic computation.  This computation was understood and logically implemented by many scientists and engineers.

We use Complements  in digital computers for almost  simplifying the subtraction operation and for logical manipulations and computations.

There are two types of complement for each base-r system:

(1) the r’s complement
(2) the (r-1)’s complement

When the value of the base is substituted, the two types receive the names 2’s and 1’s complementary for binary numbers, or 10’s and 9’s complement for decimal numbers.

Now let us see how this happens

The r’s complement

Given a positive number N in base r with an integer part of n digits, the r’s complement of N is defined as rn – N for N#0 and 0 for N=0.  The following numerical example will help clarify the definition.

The 10’s complement of (89654)10 is 105- 89654 = 10346.
The number of digits in the number is n = 5.
The 10’s complement of (0.9287)10 is 1 - 0.9287 = 0.0713
No integer part 10n = 100 is 1

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