Foundations of digital logic: which mathematical system did Claude Shannon apply to describe and analyze the behavior of electronic switching circuits, forming the basis of modern digital design?

Introduction / Context:
Claude Shannon's master's thesis revolutionized electrical engineering by linking logic and circuit design. He showed that binary relay and switching circuits could implement logical propositions, enabling systematic analysis and synthesis of digital systems—the conceptual foundation of modern computing hardware.

Given Data / Assumptions:

• We are seeking the mathematical logic system Shannon used.
• The context is electronic switching circuits (relays, gates).
• Options include programming languages and AI fields that are unrelated to circuit logic.

Concept / Approach:

Boolean algebra, with variables taking values 0 and 1 and operations AND, OR, NOT, provides a perfect abstraction for circuit states and gate behavior. Shannon mapped logical expressions to relay circuits, enabling algebraic minimization and reliable design practices still taught today (K-maps, algebraic simplification, logic synthesis).

Step-by-Step Solution:

Verification / Alternative check:

Electronics and computer engineering curricula universally credit Boolean algebra as the theoretical basis for digital logic design per Shannon's pioneering work.

Why Other Options Are Wrong:

LISP/XLISP: Programming languages; unrelated to relay logic foundations.

Neural networking: A modeling paradigm; not the algebra Shannon applied.

None: Incorrect because the correct system is well known.

Common Pitfalls:

Assuming a programming language was involved; Shannon's contribution was mathematical abstraction directly tied to circuits.

Final Answer:

Boolean algebra