Programmable controller operation: which statement correctly describes how a PLC manages logic during runtime and what it can do?

Introduction / Context:
Programmable logic controllers (PLCs) execute user programs cyclically, scanning inputs, solving logic, and updating outputs. Internally, they store the state of coils, contacts, counters, timers, and registers in memory areas that the CPU reads and writes every scan. Modern PLCs also support arithmetic and advanced instructions beyond simple relays.

Given Data / Assumptions:

• We compare claims about PLC memory and capabilities.
• Latched states can be implemented in software without external hardware relays.
• Arithmetic and logical operations are routine in PLC instruction sets.

Concept / Approach:
PLC memory maps hold discrete bits (coils/contacts), timer/counter accumulators, integers, floating-point values, and more. Latching behavior is achieved using set/reset (latch/unlatch) instructions or retentive memory bits. Arithmetic instructions (ADD, SUB, MUL, DIV) and functions (compare, scale, PID) are common, enabling computation inside the controller without external devices.

Step-by-Step Solution:
Evaluate A: PLCs maintain logic states in RAM/NVRAM—true.Evaluate B: External latching relays are optional; internal latch instructions suffice—false as a requirement.Evaluate C: PLCs can perform math—false.Therefore select A as the only correct statement.

Verification / Alternative check:
Vendor manuals (Allen-Bradley, Siemens, Omron) document memory areas and arithmetic instructions, confirming internal state and computational capability.

Why Other Options Are Wrong:
B incorrectly mandates hardware where software latches are standard. C incorrectly denies arithmetic support.

Common Pitfalls:
Confusing physical relay behavior with software coils; assuming latching always requires hardware; overlooking scan-based updates that maintain memory states.

Final Answer:
All of the logic status is maintained in memory.