in Theory of Computation
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plzz expain this machine how it is working 

machine is Addition of two binary numbers

in Theory of Computation
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Here states q0,q1 are adding two bits when no carry is generated. q2,q3 are adding states when carry generated from previous state.

Take an example suppose -

we want to add A=110001 B= 111001

 

A=  1        1            0            0          0          1

B= 1         1            1            0          0          1

1   1         0            1            0           1         0

q2->q3 q1->q2 q0->q1 q1->q0 q2->q1 q0->q2

 

end carry is ignored hence the answer. Hope it helps!