Step 1: Understanding the Question:
The question asks to identify the slowest logic gate family (the one with the largest propagation delay) among the given digital logic families.
Step 2: Key Formula or Approach:
The speed of a logic family is characterized by its propagation delay ($t_{pd}$), which is the time delay between the $50\%$ point of the input transition and the $50\%$ point of the corresponding output transition.
Lower propagation delay means a faster logic family.
Step 3: Detailed Explanation:
• ECL (Emitter Coupled Logic): This is the fastest logic family because its transistors operate in the active (non-saturated) region, eliminating storage time delays. Its propagation delay is typically sub-nanosecond ($0.5\text{ ns} - 1\text{ ns}$).
• TTL (Transistor-Transistor Logic): This is a saturated logic family, but Schottky clamping (Schottky TTL) prevents deep saturation, achieving propagation delays of $2\text{ ns} - 10\text{ ns}$.
• $I^2L$ (Integrated Injection Logic): Bipolar logic family designed for high packing density with moderate speed.
• CMOS (Complementary Metal-Oxide-Semiconductor): Classical CMOS (especially older series like 4000) has a relatively slow speed because of the high input capacitance of the MOS gates and limited driving current. Its propagation delay is typically in the range of $15\text{ ns} - 50\text{ ns}$ depending on supply voltage, making it the slowest among the classic logic families listed.
Step 4: Final Answer:
The slowest logic gate family is CMOS, which corresponds to Option (C).