Design a sequential circuit with two d flip-flops a and b, and one input x_in.

(a)when xin = 0, the state of the circuit remains the same. when x_in = 1, the circuit goes through the state transitions from 00 to 01, to 11, to 10, back to 00, and repeats.

(b)when xin = 0, the state of the circuit remains the same. when x_in =1, the circuit goes through the state transitions from 00 to 11, to 01, to 10, back to 00, and repeats.

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Explanation:

The question is basically asking you to build a 2-bit asynchronous counter.

What the counter does is it increase it's value by 01₂ every clock pulse. So at 0₂, nothing happens, but at 1₂ it'll count up by 1. It then reset to 00₂ when it overflows.

The design for it is pretty much universal so I kinda did this from memory.

a.) A count-up counter (from 00-11) is simply made by connecting Q' to D, and the output of the previous DFF to the clock of the next one.

b.) A count-down counter (from 11-00) is simply made by using the same circuit as the count-up counter, but you connect Q' to the clock instead of Q.