Input signal A and B are applied to the input terminals of the 'dotted box' set up shown here. Ley y be the final output signal from the box. What are the wavefroms of the signal labelled as `C_(1)` and `C_(2)` within the box giving (in brief) the reasons for getting these wave forms. Hence draw the waveform of the final output signal y. Give reasons for your choice. Write the relation between the total output y and the input signals A and B?

Explanation

Here gate I is NAND gate working as NOT gate, gates II and IV and AND gates, gate III is NOT gate and V is NOR gate.
Boolean expression for `C_(1)=barA`.B
Boolean expression for `C_(2)=A.barB`
`:.` Output `y=bar(C_(1)+C_(2))=bar(A.B+A.barB)`
Truth table of the circuit is given below (see ahead).
The wave forms `C_(1), C_(2)` and y are shown in Fig. below

`|{:(Time,A,B,barA,barB,C_(1)=,C_(2)=,y=),("interval",,,,,bar(A).B,A.barB,bar(C_(1)+C_(2))),("For"0 "to" 1,1,0,0,1,0,1,0),("For"1 "to"2,1,1,0,0,0,0,1),("For"2"to"3,1,1,0,0,0,0,1),("For"3"to"4,0,0,1,1,0,0,1),("For more",1,0,0,1,0,1,0),(than 4,,,,,,,):}:|`