1. 1. A sequential circuit has two inputs (A₁ and A₀) and one output (B). The output B = 1 every time the input pattern “312” (11/01/10) is observed. Otherwise B is 0.

1. a) Assuming the circuit is implemented as a Moore machine, draw the corresponding state diagram.

b) Obtain the state diagram (Use binary encoding to represent states).

c) Derive flip-flop and output equations. Use D flip-flops. Do not draw the circuit.

2.A sequential circuit has two inputs (A₁ and A₀) and one output (B). The output B = 1 every time the input pattern “312” (11/01/10) is observed. Otherwise B is 0. This is the same circuit as in the previous question. Now draw the state diagram using Mealy machine approach.

1. 3. Consider the following sequential circuit and the timing values, t_P,FF = t_P,XOR = 200.0 ps, t_P,AND = t_s = 100.0 ps, and t_h = 150.0 ps.

a. Find the maximum clock frequency that can be applied to the circuit.

b. Is hold time violated in the circuit? Why or why not? Express the hold time violation condition.

1. 4. F(x, y, z, t) = P (0, 1, 4, 6, 8, 9, 10, 12, 14, 15)

1. a. Implement the circuit using a decoder and an or gate.

b. Implement the circuit using the smallest multiplexer. (Do not use any other logical element)

X D Q D Q Y Yo