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Given JK FlipFlop, For J=0 and K=0,FF nextstate =  previous state

Initally QA = 0,QA' = 1 

so UP counter is initated and Q1 Q0 = 00 ,01,10,11

Now when 11 is seen, Y3 = (Q1.Q0)' = 0 occurs 

As preset is active low as soon as Y3 input of preset is 0,preset takes place.

This preset sets the value of QA = 1, thus Now DOWN counter takes place 

The count sequence of down counter is 10,01,00

Again same sequence repeats as above 

Here we want only output when  8 clock pulses are applied so 0,1,2,3,2,1,0,1.

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