Obtain 1's and 2's complement of 1010 using only four-digit representation.

Solution:

1's complement: 1's complement of 1010 is 

Please note that wherever you have a digit 1 in number then complement contains 0 for that digit and vice versa. In other words to get 1's complement of a binary number we only have to change all 1's of the number to 0 and all zeros to 1's. This can be done by complementing every bit of binary number.

2's complement: 

Adding 1 in 1's complement will produce 2's complement

The 2's complement can also be getting by not complementing least significant zeros till first 1 is encountered. This 1 is also not complemented. After this 1 rest of all bits are complemented on left.

Consequently 2's complement of given number (using this method) must be (you can check it by obtaining 2's complement as we have done in the illustration).