$[25$ pts$]$ Design a sequential circuit which calculates the $n-$th $P-$number. The $n-$th

$P-$number is defined as:

$P_n=P_{n-1}+P_{n-2}+P_{n-3},$

where $P_0=0,P_1=0,P_2=1,P_3=1,P_4=2.$ With a start signal you input $n$ to the

circuit.

a$.7pts$ Give the algorithm in a pseudo$-$code form.

b$.[8$ pts$]$ Built the ASM chart for your circuit.

c$.[10$ pts$]$ Design the control unit of your ASM using a minimum number of D$-$type

flip$-$flops and combinational circuit elements.