Assignment 33 (Assigned December 3)

Using the data path given in class, give the sequence of steps for the computation

r(x) = p(f(x),h(x)).

You are to design the control for a circuit to compute

r(x) = f(h(p(g(x),p(x,h(x))))).

Give your answer in the form of a state diagram and a table for the output logic required to cause the datapath to compute r(x). You may give your output logic in register transfer form. Assume the last state in your state machine is an orbit state. Assume that each state in your state diagram takes one time unit. Also, give a timing diagram to illustrate the behavior of the computation. Recall that a register transfer occurs at the end of the state in which it appears so the register transfer operation associated with state S0 is A,B ß x.

We want to design a sequential circuit to compute

r(x) = g(g(f(x),h(x)),f(h(x)))

using (combinational) modules that compute g(x,y), f(x), and h(x).

Draw a data dependencies graph for r(x).

Suppose you are allowed to use at most one g(x,y) module in your design for the circuit to compute r(x). Does this limitation require the addition of nonessential precedence constraints to the precedence graph for cone computation of r(x)? Briefly explain.

Suppose you are allowed to use at most one f(x) module in your design for the circuit to compute r(x). Does this limitation require the addition of nonessential precedence constraints to the precedence graph for cone computation of r(x)? Briefly explain.