Introduction / Context:
In TTL logic, the primitive most directly realized at the transistor level is typically NAND (or NOR in some families), not AND. Recognizing which primitive is “simplest” affects how complex functions are built and how many packages a design needs.
Given Data / Assumptions:
- TTL families commonly provide NAND gates as fundamental building blocks.
- An AND function generally requires a NAND followed by an inverter (or an equivalent transformation).
- Complexity is judged by transistor count and stage count, not just the name of the logic operation.
Concept / Approach:
Because TTL input stages and totem-pole outputs lend themselves naturally to NAND, AND is not the simplest. Implementing AND often involves extra inversion, which increases transistor count and propagation delay.
Step-by-Step Solution:
Identify primitive → NAND is most natural in TTL.Implement AND → NAND followed by inversion (or De Morganʼs transformations).Therefore AND is not the simplest, contradicting the statement.
Verification / Alternative check:
Standard TTL families (74xx) offer plentiful NAND packages; AND versions exist but typically incur extra stages internally.
Why Other Options Are Wrong:
Correct: Would misrepresent TTL gate economics.Only correct for Schottky TTL: Schottky speeds up devices but does not change the primitive.Only correct at low fan-in: Primitive preference remains NAND.
Common Pitfalls:
Equating boolean simplicity with hardware simplicity.Ignoring internal inversion required for AND in TTL.
Final Answer:
Incorrect
Discussion & Comments