Address space calculation: with 14 address lines, how many unique memory locations can be addressed?

Introduction / Context:
Address lines determine how many distinct locations a processor can reference in memory-mapped systems. Each address bit doubles the addressable space because it represents a binary choice (0 or 1). Understanding this exponential relation is essential for estimating memory capacity and designing decoders.

Given Data / Assumptions:

• Number of address bits, n = 14.
• Each unique address points to one memory location (often a byte or word depending on architecture).
• No banking or segmentation tricks—just pure binary addressing.

Concept / Approach:
The number of unique addresses is 2^n. With n=14, compute 2^14. This is a power-of-two calculation commonly encountered in digital design (e.g., 1K = 2^10 = 1024).

Step-by-Step Solution:

Verification / Alternative check:
Binary counting from 0 to 2^14 − 1 yields 2^14 distinct patterns; 2^14 − 1 = 16,383 is the maximum address value when starting from zero, confirming 16,384 total addresses.

Why Other Options Are Wrong:

Common Pitfalls:
Mixing up address count with maximum address value; forgetting that counting starts at zero, which still yields 2^n distinct addresses.

Final Answer:
16,384