Complements of Numbers: Maths of Binary Number Subtraction for GIS Processing (Especially for GATE-Geospatial 2022)

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There are two types of complements for each base- system:

This Diagram Shows Two Types of Complements

There are two complements in any number system; namely, base՚s complement and (base -1) ‘s complement. The base՚s complement and (base - 1) ’ s complement of a number is base , having digit capacity, and are defined as and , respectively.

The complement addition process is clarified here with the help of decimal and binary number systems. In decimal and binary number systems the base ′ s and (base - 1) ′ s complements are called 10 ′ s complement, 9 ′ s complement and 2 ′ s complement, 1 ′ s complement, respectively.


Subtract 256 from 512 with 5-digit capability, using 10՚s complement method

Here, 00512 is the minuend and 00256 is the subtrahend

Now, 10՚s complement of


(by ignoring the carry 1 from the MSD position)


Subtract 256 from 512 with 5-digit capability, using 9՚s complement method

Now, 9՚s complement of


In case of binary, if we interchange 0s by 1s and 1s by 0s of the bit patterns, we get the corresponding bit patterns of 1՚s complement.


Subtract 00111 (7) from 01001 (9) with 5-bit capability, using 1՚s complement method

Now, 1՚s complement of subtrahends



Subtract from with 5-bit capability, using 2՚s complement method.

This Image Shows Example of 2՚s Complement Addition


01001 (minuend)

00111 (subtrahend)

2՚s complement of subtrahend is


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