Digital Electronics - Serial Two's Complementer Circuit

Design a one input, one output serial 2’s complementer. The circuit accepts a string of bits from the input and generates the 2’s complement at the output. The circuit can be reset synchronously to start and end the operation.


Hint: - 2’s complement of a number can be obtained by keeping the least significant bits as such until the first 1, and then complementing all bits
eg: 001010 → 110110

Solution:
State diagram of the design: Let A, B be the two states representing the output states of a D flipflop.


Implementation of the state diagram..
Input(x) Present State Next State D-Input Output
0 A = 0 A = 0 A = 0 0
0 B = 1 B = 1 B = 1 1
1 A = 0 B = 1 B = 1 1
1 B = 1 B = 1 B = 1 0


So output Z=input(x) XOR Present State
D-input = input(x) OR Present State



Written by: Shiju