Power of 2 Table

System Design FundamentalsEntrysystem-design

The Question

What are the key powers of 2 every engineer should know?

What a Strong Answer Covers

• All five.

Senior-Level Answer

Powers of 2 are the vocabulary of capacity estimation. Every storage, memory, and bandwidth number is ultimately expressed in multiples of 2^n bytes. Internalizing this table prevents unit errors under interview pressure.

**The core table:**

| Power | Value | Common name | Practical example | |---|---|---|---| | 2^10 | 1,024 | 1 KB | Short text field, tweet | | 2^20 | ~1 million | 1 MB | Small image, 1 min MP3 | | 2^30 | ~1 billion | 1 GB | Movie file, RAM on a phone | | 2^40 | ~1 trillion | 1 TB | Laptop SSD, daily log volume | | 2^50 | ~1 quadrillion | 1 PB | Large data warehouse |

**Why approximate with 10^3, 10^6, 10^9?** 2^10 = 1,024 ≈ 10^3. This 2.4% error compounds: 1 GB is actually 1.07 × 10^9 bytes. For estimation purposes this is irrelevant — you are trying to distinguish 'do I need 1 GB or 1 TB', not measure precisely.

**Derived conversions that appear in interviews:** - 1 million users × 1 KB record = 1 GB - 1 billion records × 1 KB = 1 TB - 1 billion records × 1 MB (image) = 1 PB - 8 bits = 1 byte → 1 Gbps = 125 MB/s - A 64-bit integer = 8 bytes; UUID = 16 bytes; SHA-256 hash = 32 bytes

**Practical anchors:** - L1 cache: ~32 KB; L2: ~256 KB; L3: ~8 MB - Typical server RAM: 64–256 GB - NVMe SSD: 1–4 TB, ~3 GB/s throughput - S3 object max size: 5 TB

Memorise: 10, 20, 30, 40, 50 → KB, MB, GB, TB, PB. Everything else derives from this.

What Separates a 2/3 from a 3/3

Common Mistakes

• Confusing MB (megabytes) with Mb (megabits) in bandwidth calculations
• Using exact values (1,024) in estimations where ≈1,000 is faster and sufficient
• Not knowing that 1B records × 1KB = 1TB — a foundational derived fact
• Forgetting that storage vendors use SI (1 TB = 10^12) while OS tools use binary (1 TiB = 2^40)

Follow-Up Questions

• How many bytes is a UUID and why does it matter for storage estimation? — 16 bytes — at 1B users that's 16 GB just for IDs; relevant when estimating index sizes.
• Convert 10 Gbps to MB/s. — 10 Gbps ÷ 8 = 1.25 GB/s = 1,250 MB/s.
• If your database has 100M rows each 1KB average, how much storage do you need? — 100M × 1KB = 100GB for data; add 20–30% overhead for indexes, giving ~130GB.
• What is the difference between a GB and a GiB? — GB = 10^9 bytes (SI); GiB = 2^30 bytes = 1.073 × 10^9 bytes (binary). Disk manufacturers use GB; OS tools report GiB.

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