NOR-based S-R latch operation — identifying the hold (no-change) input combination: For the classic cross-coupled NOR gate S-R latch, which S and R input combination produces the HOLD (no state change) condition?

Introduction / Context: The simplest memory element in digital logic is the S-R latch constructed from two cross-coupled NOR gates. Knowing which input combinations set, reset, or hold the state is essential for analyzing asynchronous hazards and for building higher-level sequential elements.

Given Data / Assumptions:

• Latch type: two NOR gates cross-coupled, inputs labeled S (set) and R (reset).
• Inputs are active-HIGH (typical for NOR-based latches).
• Outputs are Q and Q’ with mutual feedback.

Concept / Approach: For a NOR-latch, active-HIGH S forces Q = 1 (set), and active-HIGH R forces Q = 0 (reset). When both S and R are LOW, neither gate’s direct input asserts, so feedback maintains the existing state. If both S and R are HIGH simultaneously, both outputs are driven LOW, producing an invalid/forbidden condition because Q and Q’ are no longer complements after inputs return LOW.

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