ITPEC FE Morning October 2018 Question 25

Fixed-Length Code Capacity — find minimum code length for a growing customer base.

Customers after 3 years: 8,000 × 1.2³ = 13,824

Code uses 26 uppercase letters (A–Z), so capacity = 26^n:
- 26² = 676 — not enough
- 26³ = 17,576 ≥ 13,824 — sufficient

Answer: a) 3

Why not others:
- (b) 4 — 26⁴ = 456,976, works but not minimum
- (c) 5 — 26⁵, far more than needed
- (d) 6 — 26⁶, far more than needed

Key rule: Find smallest n where alphabet_size^n ≥ total_items.

AI-generated — may contain errors