Q. 5.17: Design a one-input, one-output serial 2’s complementer. The circuit accepts a string of
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state table description:
at the
state table description:
at the beginning of the solution, I have explained one example:
the number is 01001110101100 and its 2's complement is 10110001010100
now observe the 2's complement carefully.
from RHS, the number and 2's complement are the same until first 1 is arrived. i.e., when we have input is zero and present state (PS) is zero the 2's complement output is zero, and the next state (NS) is also zero. this means, the 1st row in the state table.
now consider the 2nd row in state table:
we have PS=0 and input =1, this means we got the 1st 1 from RHS. so, output=input=1.
3rd row: PS=1, input=0
after arrival of a 1 as PS in the 2's complement sequence, if the input is zero then we have to complement the PS, i.e., output = complement(PS). thus the NS =1
4th row: PS=1, Input=1:
the output = complement(PS)=0
NS =1, because we have already passed the first 1 in the sequence.
NB: PS is seen from 2's complement sequence and input is seen from the given number under consideration. For finding (n+1)th output, the PS is (n)th bit from output sequence, and the input is (n+1)th bit from given number counting from RHS.
Q. 5.17: 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 asynchronously to start and end the operation.
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Dhiman Kakati
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