Which device can realize any Boolean function of the input variables by effectively generating every possible AND (minterm) product term and then selecting among them?

Introduction / Context:
Digital designers often compare classic programmable devices by how their internal arrays are organized. The ability to realize any Boolean function directly depends on whether the device can make all minterms (AND products) available for selection.

Given Data / Assumptions:

• We want a device that generates every possible AND product term of the inputs.
• Then it produces the desired function by OR-ing selected terms.
• Options include GAL, SOP, PROM, and LAB.

Concept / Approach:
A PROM uses a full decoder that generates all 2^n minterms of the n inputs, effectively creating every possible AND term. The memory array then stores desired output bits for each minterm; reading the addressed word is equivalent to forming an OR of the selected minterms. Thus a PROM can implement any combinational truth table directly. A GAL is a small SPLD with limited product terms; SOP is a form, not a device; LAB is a cluster inside some FPGAs/CPLDs, not a standalone device class.

Step-by-Step Solution:
Recognize that a full decoder + ROM can represent any truth table.PROM architecture provides all minterms via address decoding.Therefore, PROM fits the requirement of “generates every possible AND term.”

Verification / Alternative check:
Textbooks routinely state that a ROM/PROM is a universal combinational device because it stores the output for every input combination.

Why Other Options Are Wrong:
GAL has limited product terms per output. SOP is not hardware. LAB is a sub-block and does not inherently generate all minterms on its own.

Common Pitfalls:
Confusing logical forms (SOP) with hardware implementations; assuming any PLD always has “all minterms” available (only PROM/PLA style guarantees this).

Final Answer:
PROM