Consider a 4-bit Johnson counter with an initial value of 0000. The counting sequence of this counter is

The minimum number of $$JK$$ flip-flops required to construct a synchronous counter with the count sequence $$\left( {0,0,1,1,2,2,3,3,0,0,...} \right)$$ is ____________.

Let $$k = {2^n}.$$ A circuit is built by giving the output of an ݊$$n$$-bit binary counter as input to an $$n$$-to-$${2^n}$$ bit decoder. This circuit is equivalent to a

You are given a free running clock with a duty cycle of $$50$$% and a digital waveform $$f$$ which changes only at the negative edge of the clock. Which one of the following circuits (using clocked $$D$$ flip-flops) will delay the phase of $$f$$ by $${180^0}?$$