1's Complement vs 2's Complement
Complements are used in digital computers in order to simply the subtraction operation and for the logical manipulations. For the Binary number (base-2) system, there are two types of complements: 1’s complement and 2’s complement.
1’s Complement of a Binary Number
There is a simple algorithm to convert a binary number into 1’s complement. To get 1’s complement of a binary number, simply invert the given number.
2’s Complement of a Binary Number
There is a simple algorithm to convert a binary number into 2’s complement. To get 2’s complement of a binary number, simply invert the given number and add 1 to the least significant bit (LSB) of given result.
Differences between 1’s complement and 2’s complement
These differences are given as following below −
1’s complement
| 2’s complement
|
|---|
To get 1’s complement of a binary number, simply invert the given number.
| To get 2’s complement of a binary number, simply invert the given number and add 1 to the least significant bit (LSB) of given result.
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1’s complement of binary number 110010 is 001101
| 2’s complement of binary number 110010 is 001110
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Simple implementation which uses only NOT gates for each input bit.
| Uses NOT gate along with full adder for each input bit.
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Can be used for signed binary number representation but not suitable as ambiguous representation for number 0.
| Can be used for signed binary number representation and most suitable as unambiguous representation for all numbers.
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0 has two different representation one is -0 (e.g., 1 1111 in five bit register) and second is +0 (e.g., 0 0000 in five bit register).
| 0 has only one representation for -0 and +0 (e.g., 0 0000 in five bit register). Zero (0) is considered as always positive (sign bit is 0)
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For k bits register, positive largest number that can be stored is (2(k-1)-1) and negative lowest number that can be stored is -(2(k-1)-1).
| For k bits register, positive largest number that can be stored is (2(k-1)-1) and negative lowest number that can be stored is -(2(k-1)).
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end-around-carry-bit addition occurs in 1’s complement arithmetic operations. It added to the LSB of result.
| end-around-carry-bit addition does not occur in 2’s complement arithmetic operations. It is ignored.
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1’s complement arithmetic operations are not easier than 2’s complement because of addition of end-around-carry-bit.
| 2’s complement arithmetic operations are much easier than 1’s complement because of there is no addition of end-around-carry-bit.
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Sign extension is used for converting a signed integer from one size to another.
| Sign extension is used for converting a signed integer from one size to another.
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Published on 21-Feb-2019 15:03:36
