Introduction:
The figure of merit of a logic family is a measure of its overall performance and efficiency. It helps in comparing different logic families and selecting the most suitable one for a particular application. The figure of merit is determined by various parameters such as gain, bandwidth, propagation delay time, power dissipation, fan-out, noise margin, etc. Among these parameters, the product of propagation delay time and power dissipation is considered as the figure of merit for a logic family.

Explanation:
Propagation delay time and power dissipation are two critical factors that significantly affect the performance and efficiency of a logic family. Let's understand why the product of these two parameters is used as the figure of merit:

Propagation Delay Time:
Propagation delay time is the time taken for a logic signal to propagate through a gate or a circuit from the input to the output. It indicates how quickly the logic family can process the input and provide the corresponding output. A shorter propagation delay time is desirable as it allows for faster operation and better response time.

Power Dissipation:
Power dissipation refers to the amount of power consumed by the logic family to perform its operations. It is an important factor to consider as excessive power dissipation can lead to heating issues, reduced overall efficiency, and increased energy consumption. Minimizing power dissipation is crucial for ensuring better performance and reducing energy costs.

Product of Propagation Delay Time and Power Dissipation:
The product of propagation delay time and power dissipation gives an overall measure of the performance and efficiency of a logic family. It takes into account both the speed of operation (propagation delay time) and the power consumed (power dissipation) by the logic family.

By multiplying these two parameters, we get a figure of merit that reflects the trade-off between speed and power consumption. A logic family with a lower product value would be considered more efficient as it achieves faster operation with lower power consumption.

Conclusion:
In summary, the product of propagation delay time and power dissipation is used as the figure of merit for a logic family because it captures the trade-off between speed and power consumption. It provides a comprehensive measure of the overall performance and efficiency of the logic family, allowing for easy comparison and selection among different logic families.