Hazards and races: in which type(s) of digital circuits can dynamic race hazards occur due to unequal propagation delays along multiple paths to an output?

Introduction / Context:
In real hardware, signals take time to propagate through gates and wires. When multiple paths with different delays drive the same output expression, temporary spurious transitions—called hazards—can appear. Understanding where dynamic race hazards arise helps engineers design glitch-free logic, especially for asynchronous interfaces.

Given Data / Assumptions:

• Dynamic hazards are characterized by multiple unwanted transitions during a single input change.
• We distinguish hazards in combinational logic from race conditions in sequential elements.
• We assume standard gate-level realizations and non-zero propagation delays.

Concept / Approach:
Hazards are typically classified as static-0, static-1, and dynamic. Static hazards cause one spurious pulse; dynamic hazards cause multiple toggles when an output should make a single transition. These are properties of combinational networks implemented with real gates. Sequential circuits exhibit races (e.g., race-around in latches), but that phenomenon is distinct from the classical hazard types defined for combinational networks.

Step-by-Step Solution:
Model the Boolean function realized via multiple gate-level paths.Assign unequal delays to different paths.Observe that an input transition may cause an output to oscillate before settling (dynamic hazard).Note: while sequential circuits have “race” issues, the canonical hazard taxonomy refers to combinational logic.

Verification / Alternative check:
Karnaugh-map-based hazard analysis and consensus term insertion techniques are taught specifically for combinational circuits to remove dynamic and static hazards.

Why Other Options Are Wrong:
Sequential circuits only: conflates race conditions in storage elements with hazards in logic networks.Both combinational and sequential: overgeneralizes the dynamic hazard definition.None: hazards are well-documented in combinational implementations.None of the above: a correct option exists.

Common Pitfalls:
Mixing up hazard terminology with latch races; ignoring that proper synchronization or adding consensus terms can eliminate hazards in combinational paths.

Final Answer:
Combinational circuits only