STA Interview Question: Propagation and Contamination Delay

Suppose we are building circuits using only the following three components:

• inverter: tcd = 0.5ns, tpd = 1.0ns, tr = tf = 0.7ns
• 2-input NAND: tcd = 0.5ns, tpd = 2.0ns, tr = tf = 1.2ns
• 2-input NOR: tcd = 0.5ns, tpd = 2.0ns, tr = tf = 1.2ns

Consider the following circuit constructed from an inverter and four 2-input NOR gates:

1. What is t_PD for this circuit?
   
2. What is t_CD for this circuit?
3. What is t_PD of the fastest equivalent circuit (i.e., one that implements the same function) built using only the three components listed above?

Solution:

1. t_PD for the circuit is the maximum cumulative propagation delay considering all paths from any input to any output. In this circuit, the longest path involves three 2-input NAND gates with a cummulative t_PD = 6ns.
2. t_CD for the circuit is the minimum cumulative contamination delay considering all paths from any input to any output. In this circuit, the shortest path involves two 2-input NAND gates with a cumulative t_CD = 1ns.
3. 
   
   The most straightforward way to determine the functionality of a circuit is to build a truth table:

   A  B  | OUT
   ======|=====
   0  0  |  1
   0  1  |  0
   1  0  |  1
   1  1  |  0
   

   from which we can see that OUT = not B. We can implement this with a single inverter that has a t_PD = 1ns.