Question

5. [10 Pts] Determine the critical path in the following circuit. Also determine the propagation delay and contamination delay. Use the gate delays given in the table below Gate NOT 2-input NAND 3-input NAND 2-input NOR 3-input NOR 2-input AND 3-input AND 2-input OR 3-input OlR Ipd (ps) 15 20 30 30 45 ed (ps) 10 15 25 25 35 25 30 30 45 40 40

Answer 1

The given circuit is a combinational circuit. Each gate in this circuit has a propagation delay (t_pd) and a contamination delay (t_cd) as given in the question.

Definition of each term

Term Definition Propagation Delay (tpd) The propagation delay is the maximum time taken from the instant of change in the input of a gate (or a combinational circuit) until the output REACHES its final state. Contamination Delay (tcd) The contamination delay is the minimum time taken from the instant of change in the input of a gate (or a combinational circuit) until the output STARTS to change its state. It is the best-case value as it indicates the least response time that the circuit would take to an input change. Critical Path The critical path of a combinational circuit is the path in which sum of propagation delays is maximum, i.e., the LONGEST PATH. It is the worst-case value indicating the maximum response time of the circuit to an input change.

Now, each gate is labelled as 1, 2, ..., 6 as in the below figure with its corresponding propagation delay. The sum of the propagation delays along the path highlighted in RED has the maximum value compared to the other paths.

Propagation delay (tpd) is labelled under each gate 30 ps 3 20 ps 6 30 ps 20 ps 4 F. 30 ps Critical Path is highlighted in RED 30 ps

Hence, the critical path is :

Input F or G -> 2 -> 4 -> 5 -> 6 -> Output Y

The propagation delay of a combinational circuit is the sum of the t_pds along its critical path.

Therefore, t_pd2 + t_pd4 + t_pd5 + t_pd6 = 30 + 30 + 30 + 20 = 110 ps

Propagation Delay = 110 ps

The contamination delay of a combinational circuit is the sum of t_cds along its shortest path.

From the figure below, the sum of the contamination delays along the path highlighted in BLUE has the least value compared to the other paths,

i.e, the path, INPUT D ->   3 -> 5 -> 6 -> Output Y

Contamination delay (tcd) is labelled under each gate В 1 25 ps 3 15 ps -t 6 25 ps 15 ps 4 25 ps 25 ps Shortest path is highlighted in BLUE

Therefore, t_cd3 + t_cd5 + t_cd6 = 15 + 25 + 15 = 55 ps

Contamination Delay = 55 ps