Capabilities of digital circuits: “Digital circuits cannot perform logic comparisons because the circuit can have only one of two values at any instant.” Evaluate this claim.

Difficulty: Easy

Correct Answer: Incorrect

Explanation:


Introduction / Context:
Logic comparisons such as equality, greater-than, or parity checks are core tasks for digital hardware. The statement claims digital circuits cannot compare because they have only two values at any instant—a misunderstanding of how multi-bit logic and Boolean operations work.


Given Data / Assumptions:

  • Digital signals are binary at any node (0 or 1).
  • Comparisons operate on multi-bit words using gates.
  • Timing is adequate for valid logic evaluation.


Concept / Approach:
Digital comparators cascade basic gates to implement functions like A == B, A > B, and A < B. Even though each signal is binary, networks of gates can evaluate conditions over multiple bits in parallel. CPUs, ALUs, and dedicated comparator ICs are practical embodiments of this principle.


Step-by-Step Solution:

Define comparison as a Boolean function over bit vectors.Implement equality by XORing each bit pair and ORing the results, then invert for equality.Implement greater-than via prioritized subtraction/propagate logic.Conclude that digital logic readily performs comparisons.


Verification / Alternative check:
Standard ICs (e.g., 74xx85 magnitude comparators) prove that two-value logic readily implements complex comparisons reliably and quickly.


Why Other Options Are Wrong:

  • Correct: Contradicts real hardware capabilities.
  • Analog comparators: Analog components compare voltages, but digital comparators operate on bits.
  • Temperature/clock excuses: Irrelevant to the logical possibility of comparison.


Common Pitfalls:
Mistaking signal discreteness (two levels) for functional limitation; in fact, Boolean algebra enables arbitrary logic, including comparisons, with binary signals.


Final Answer:
Incorrect

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