2) A three-bit synchronous binary counter is required to count backwards and forwards within the range 000111. The input x controls the direction of counting. The counter should be incremented at the next clock pulse if x =1. It should be decremented if x=0. Also note that the counter has to cycle back to 000 after 111, if it is counting forward. Similarly, in backwards counting mode, it has to switch to 111 after the 000 state. Design such a counter in four different ways; namely, using RS, JK, T and D flip-flops. Follow the steps below. Simplify the combinational part of the circuit so as to have as few numbers of gates as possible in each case. You can use all (two-input or multi-input) standard gates (i.e. NOT, AND, OR, NAND, NOR, X-OR X-NOR) in your design. e) Design the counter using D flip-flops: i) Obtain the state equations in a simplified form. ii) Sketch the circuit diagram