2’s Complement

There are two method finding of 2’s complement

(Most common method)

  • Method – I        
2' complement Finding Method-I

How to Find 2’s Complement by Method-I

Step -1:  Take 1’s complement of each digit.(Opposite all the bits from 0 to 1 and 1 to 0 for making it in 1’s complement.

Step- 2: ADD one in the LSB(Least significant bit)  as shown above in the diagram.

Step-3: Then it becomes in the form of 2’s complement.

(MOST TRICKY METHOD you never seen before)

  • Method – II
2's Complement Finding by Trick

How to Find 2’s Complement by Method-II

Step -1: Write all the digit the same as the given bit until found 1. When you see 1 in the given bit, write that 1.

Step -2 After founding 1, oppose all the bits from 1 to 0 and 0 to 1, for converting it into 2’s complement.

Step -3 Now, you can see the whole digit converted into 2’s complement.

One more example of Method- II

Operation with 2’s complement

  • Case-1: Addition of two Positive value +5 and +2
    • +5 Represents in binary ( 1 0 1 )
    • +2 Represents in binary ( 0 1 0 )

Note Computer is not understood – (negative) values so, for doing negative calculation the digit change into 2’s complement through the above method. If after calculation the result gives MSB bit 0 it denotes a positive value and if the result gives MSB bit 1 it means the value of the result is negative.

  • Case-2: Subtraction of two value +5 and -2
    • +5 Represents in binary (1 0 1 )
    • +2 Represents in binary ( 0 1 0 )
  • Convert +2 into -2 using 2’s complement
    • -2 Represents in binary ( 1 1 0 )
  • Case-3: Subtraction of two value -5 and -2
    • -5 Represents in binary ( 0 1 1 )
    • -2 Represents in binary ( 1 1 0 )

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