NAND-based S–R latch behavior at forbidden inputs: Assume an S–R latch constructed from cross-coupled NAND gates (active-LOW inputs labeled S̄ and R̄). If both inputs are forced to 0 at the same time, what will the two outputs (Q and Q̄) be?

Introduction / Context:
This question examines the forbidden-input behavior of a basic S–R latch implemented with cross-coupled NAND gates. Understanding how the outputs respond when both active-LOW control inputs (S̄ and R̄) are driven LOW is crucial for reliable digital design. It reinforces the difference between valid control combinations and the one invalid combination that designers must avoid when using NAND-based S–R latches.

Given Data / Assumptions:

• Latch topology: cross-coupled NAND gates forming an S̄–R̄ latch.
• Inputs are active-LOW (a 0 is an asserted Set or Reset).
• Both inputs are simultaneously 0.
• No propagation delays or analog effects are modeled beyond the ideal logic behavior.

Concept / Approach:
In a NAND-based S̄–R̄ latch, the valid operating region excludes the case where S̄ = 0 and R̄ = 0 simultaneously. When either input is asserted LOW by itself, the latch sets or resets accordingly. However, asserting both LOW forces both NAND outputs HIGH, which violates the requirement that Q and Q̄ be logical complements. This is the classic “forbidden” or invalid input combination for the NAND S–R latch.

Step-by-Step Solution:

Verification / Alternative check:
Draw the two NAND gates and apply the input levels. Each gate sees a 0 on one input, so both outputs must be 1. This direct gate-level reasoning verifies the result without needing timing diagrams.

Why Other Options Are Wrong:

• Q = 0 and Q̄ = 0: For NAND gates, a 0 on any input yields a 1 at the output, so this cannot occur here.
• Q = 1 and Q̄ = 0 or Q = 0 and Q̄ = 1: These are valid complementary states, but they do not result from the 0,0 input condition on a NAND S–R latch.
• Outputs oscillate at the clock frequency: The basic latch has no clock; oscillation is not expected from static inputs.

Common Pitfalls:
Confusing NAND- and NOR-based S–R latches; forgetting that the invalid combination differs between active-HIGH (NOR) and active-LOW (NAND) implementations; assuming a clock is present in a latch; expecting complementary outputs even under forbidden inputs.

Final Answer:
Q = 1 and Q̄ = 1