Look-up table (LUT) concept in digital design Evaluate the statement: “A look-up table is simply a truth table with all possible output connections listed with their desired input response.” Is this statement accurate for LUTs used in FPGAs and logic design?

Introduction / Context:
Look-up tables (LUTs) are the fundamental combinational logic elements in most FPGAs. Conceptually, a LUT implements a truth table by storing the desired output for every combination of its input address lines. Understanding this makes it easier to map Boolean equations to FPGA resources and to visualize how synthesis tools realize logic.

Given Data / Assumptions:

• A k-input LUT can represent any Boolean function of k variables.
• The LUT contains 2^k stored bits, each corresponding to one input combination.
• Inputs act as address lines; the stored bit at that address appears at the LUT output.

Concept / Approach:
Since each possible input vector is mapped to a predetermined output bit, a LUT is functionally equivalent to a truth table held in a small memory. Synthesis tools write these bits based on the designer’s Boolean description so that hardware performs the desired logic without enumerating explicit gate-level structures.

Step-by-Step Explanation:

Verification / Alternative check:
Vendor documentation shows LUTs implemented as SRAM/flash bits feeding a multiplexer tree. This architecture is indistinguishable from a truth table abstraction: each address selects the predefined output bit.

Why Other Options Are Wrong:

• “False” or conditions about synchronous logic/tri-state are irrelevant; LUTs are generic combinational elements.
• “Stores only state information” mischaracterizes LUTs; state storage is handled by flip-flops or block RAMs, not LUTs.

Common Pitfalls:

• Confusing LUTs (combinational) with registers (sequential).

Final Answer:
True