2. A four-bit addition machine is built with four full adders such that the carr
ID: 3672854 • Letter: 2
Question
2. A four-bit addition machine is built with four full adders such that the carry out of the first adder is the carry in to the second adder, and the carry out of the second is the carry in to the third, and so on as shown in Figure 2.
The machine has input and output registers and must complete the addition in one clock cycle.
Each full adder has the following propagation delays: 20 ps from Cin to Cout or to Sum(S), 25 ps from A or B to Cout, and 30 ps from A or B to S.
The adder has a contamination delay of 15 ps from Cin to either output and 22 ps from A or B to either output.
Each flip-flop has a setup time of 30 ps, a hold time of 10 ps, a clock-to-Q propagation delay of 35 ps, and a clock-to-Q contamination delay of 25 ps.
(a) If there is no clock skew, what is the maximum operating frequency of the circuit?
(b) If there is retiming using designated skew, what is the maximum operating frequecy of the circuit?
A2 A Cin co CLK CLK Figure 2: A four-bit addition machine.Explanation / Answer
Answer a
Tc . Tpcq + Tpd + Tsetup
Longest path:
Tc . Tpcq + 3*Tpd + Tsetup
Tc . 70 + 3*100 + 60 = 430 ps
Max Frequency = 1/Tc = 2.33 GHz
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