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- Computer Organization Tutorial
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- CO - Overview
- CO - Digital Number System
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- CO - Binary Codes
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- CO - Complement Arithmetic
- CO - Binary Arithmetic
- CO - Octal Arithmetic
- CO - Hexadecimal Arithmetic
- CO - Boolean Algebra
- CO - Logic Gates
- CO - Combinational Circuits
- CO - Sequential Circuits
- CO - Digital Registers
- CO - Digital Counters
- CO - Memory Devices
- CO - CPU Architecture
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Complement Arithmetic
Complements are used in the digital computers in order to simplify the subtraction operation and for the logical manipulations. For each radix-r system (radix r represents base of number system) there are two types of complements.
S.N. | Complement | Description |
---|---|---|
1 | Radix Complement | The radix complement is referred to as the r's complement |
2 | Diminished Radix Complement | The diminished radix complement is referred to as the (r-1)'s complement |
Binary system complements
As the binary system has base r = 2. So the two types of complements for the binary system are 2's complement and 1's complement.
1's complement
The 1's complement of a number is found by changing all 1's to 0's and all 0's to 1's. This is called as taking complement or 1's complement. Example of 1's Complement is as follows.
![1's complement](/computer_logical_organization/images/1s_complement.jpg)
2's complement
The 2's complement of binary number is obtained by adding 1 to the Least Significant Bit (LSB) of 1's complement of the number.
2's complement = 1's complement + 1
Example of 2's Complement is as follows.
![2's complement](/computer_logical_organization/images/2s_complement.jpg)
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