Given a state machine has one input x(t) and two-bit state (Q1(t), Q0(t)). The machine is described by the following state equations:
Q1(t + 1) = x(t)Q0(t) + Q0'(t)
Q0(t + 1) = Q1(t)Q0'(t) + x'(t)Q0'(t)
Use two D flip-flops and a minimal sum-of-products network to implement the machine.
(i) Fill the state table of the system.
id Q1(t) Q0(t) x(t) Q1(t+1) Q0(t+1)
0 0 0 0 0 1
1 0 0 1 0 0
2 0 1 0 0 1
3 0 1 1 0 1
4 1 0 0 1 0
5 1 0 1 1 1
6 1 1 0 1 1
7 1 1 1 1 1
(ii) Describe the design using a logic diagram. Show your derivation (K maps).