Binary Arithmetic : 1's and 2's Compliment

1's Compliment :

The 1's compliment of any binary number can be found by converting 1's into 0's and 0's into 1's. For example the binary number (1010)2 (10 in decimal) 1's  compliment is :


Now the 1's compliment of 1010 is 101.


2's Compliment :

The 2's compliment of any number can be calculated by, first converting the binary number into it's 1's compliment and then adding 1 to the Least Significant Bit (LSB) of 1's compliment number. For example Lets calculate the 2's compliment of binary number (1101010)2 (106 in decimal) 2's :

Step 1 : 1's compliment of given binary number :


Step 2 : Add 1 to Least Significant Bit


Now the binary number 0010110 is the second compliment of 1101010.


Alternative Method For Finding 2's compliment :

The 2's compliment can also be found out by using alternative method. In this method Looking from LSB side, note all the digits till the first binary 1 is encountered, after that  1's compliment all rest of the digits, and the final number is 2's compliment of that number. For example lets try to find the 2's compliment of 11011100 by the alternative method :


Now we need to 1's compliment rest of the digits or bits which are underlined.


 The 2's compliment of 11011100 is 100100




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