Foundational base — digital electronics, logic gates, and computer arithmetic are fundamentally built on which numbering system?

Introduction / Context:
Modern digital hardware represents information using discrete voltage levels mapped to symbols. The most robust and economical choice is two stable states, enabling noise-immune switching and straightforward implementation with transistors. This naturally aligns with the binary numbering system.

Given Data / Assumptions:

• Logic circuits use two distinct states (low/high).
• Voltage thresholds separate 0 from 1 to provide noise margins.
• Other radices may be used for human representation but not for core hardware operation.

Concept / Approach:
The binary system (base 2) uses digits 0 and 1. In hardware, these correspond to two voltage ranges (e.g., 0 V and +V). Boolean algebra maps logic operations (AND, OR, NOT) to simple transistor networks. While hexadecimal and octal are convenient shorthand for grouping bits (4 and 3 respectively), they are not the physical basis; they simply compress binary for readability. Decimal is used in human interfaces and BCD storage when necessary, but internal logic remains binary.

Step-by-Step Solution:

Verification / Alternative check:
Observe that memory cells, registers, and buses store and transmit bits. Groupings (nibbles/bytes) are powers of 2, reinforcing the binary foundation.

Why Other Options Are Wrong:

Common Pitfalls:
Assuming hex is “native” because of its prevalence in programming; it merely maps to 4-bit groups.

Final Answer:
Binary (base 2)