Foundations of Digital Electronics — Underlying Number System Digital electronics fundamentally operates using which numbering system for representing logic levels and data?

Introduction / Context:
Logic circuits use two distinct voltage ranges to represent information. These two states correspond naturally to a base-2 numbering system, making binary the fundamental language of digital hardware, storage, and computation.

Given Data / Assumptions:

• Logic low and logic high are the only stable states in standard digital families.
• Transistors switch between two regions to encode information reliably.
• Systems can present higher level abstractions, but the hardware building blocks are two state devices.

Concept / Approach:
Map the two physical states to symbols 0 and 1. Larger numerical bases like octal and hex are useful shorthand for compact human representation, but at the hardware level all computation decomposes into binary operations and bit patterns.

Step-by-Step Reasoning:
1) Recognize that digital storage elements hold two states.2) Relate two states to base-2 digits.3) Understand that octal and hex are only groupings of binary bits for convenience.4) Conclude that the foundational numbering system is binary.

Verification / Alternative check:
Examine truth tables, Karnaugh maps, and Boolean algebra. All of these formalisms operate over two valued logic, directly reflecting binary representation.

Why Other Options Are Wrong:

• Decimal: Used for human readability, not hardware level operation.
• Octal and hexadecimal: Helpful groupings of binary but not fundamental.

Common Pitfalls:
Assuming shorthand bases change the underlying hardware representation; in practice, everything ultimately maps to binary signals.

Final Answer:
binary