Information Units: Match Unit Name to Its Associated Logarithmic Base List I A. bit B. nat C. decit List II 10 e 2

Introduction / Context:
Information measures use logarithms with different bases, leading to familiar units: bits, nats, and decimal digits (decits). Knowing the base associated with each unit is key when converting entropy or information rates between unit systems.

Given Data / Assumptions:

• bit uses base 2 logarithms.
• nat uses base e logarithms.
• decit (also called Hartley) uses base 10 logarithms.

Concept / Approach:

Map each unit to its defining logarithm base. Conversion follows change-of-base formulas: log_b(x) = log_k(x) / log_k(b). Thus 1 nat = log_2(e) bits ≈ 1.4427 bits; 1 decit = log_2(10) bits ≈ 3.3219 bits.

Step-by-Step Solution:

Verification / Alternative check:

Entropy conversions: H_bits = H_nats / log_e(2). For decimal digits, H_bits = H_decits * log_2(10). These confirm the base associations.

Why Other Options Are Wrong:

Swapping bases produces incorrect conversion factors; for instance, treating a nat as base 10 would wildly misstate information content.

Common Pitfalls:

Confusing “decade” (frequency factor of 10) with decit (information unit) and mixing up natural logarithms with base-10 common logarithms.

Final Answer:

A-3, B-2, C-1