You might be asked to do some estimates by hand during system design interviews. For example, you might need to determine how long it will take to generate 100 image thumbnails from disk or how much memory a data structure will take.
Memorize the Powers of Two table and Latency numbers - they’re essential for quick calculations during interviews.
Powers of Two Table
Use this table for quick approximations of storage and memory calculations:
Power Exact Value Approx Value Bytes
---------------------------------------------------------------
7 128
8 256
10 1024 1 thousand 1 KB
16 65,536 64 KB
20 1,048,576 1 million 1 MB
30 1,073,741,824 1 billion 1 GB
32 4,294,967,296 4 GB
40 1,099,511,627,776 1 trillion 1 TB
Latency Numbers Every Programmer Should Know
These numbers are critical for understanding system performance:
Latency Comparison Numbers
--------------------------
L1 cache reference 0.5 ns
Branch mispredict 5 ns
L2 cache reference 7 ns 14x L1 cache
Mutex lock/unlock 25 ns
Main memory reference 100 ns 20x L2 cache, 200x L1 cache
Compress 1K bytes with Zippy 10,000 ns 10 us
Send 1 KB bytes over 1 Gbps network 10,000 ns 10 us
Read 4 KB randomly from SSD* 150,000 ns 150 us ~1GB/sec SSD
Read 1 MB sequentially from memory 250,000 ns 250 us
Round trip within same datacenter 500,000 ns 500 us
Read 1 MB sequentially from SSD* 1,000,000 ns 1,000 us 1 ms ~1GB/sec SSD, 4X memory
HDD seek 10,000,000 ns 10,000 us 10 ms 20x datacenter roundtrip
Read 1 MB sequentially from 1 Gbps 10,000,000 ns 10,000 us 10 ms 40x memory, 10X SSD
Read 1 MB sequentially from HDD 30,000,000 ns 30,000 us 30 ms 120x memory, 30X SSD
Send packet CA->Netherlands->CA 150,000,000 ns 150,000 us 150 ms
Notes
-----
1 ns = 10^-9 seconds
1 us = 10^-6 seconds = 1,000 ns
1 ms = 10^-3 seconds = 1,000 us = 1,000,000 ns
Handy Metrics
Based on the numbers above:
- Read sequentially from HDD at 30 MB/s
- Read sequentially from 1 Gbps Ethernet at 100 MB/s
- Read sequentially from SSD at 1 GB/s
- Read sequentially from main memory at 4 GB/s
- 6-7 world-wide round trips per second
- 2,000 round trips per second within a data center
Latency Numbers Visualized
Using These Numbers
When performing back-of-the-envelope calculations:
- Start with the constraint: Understand the scale (users, requests, data size)
- Use approximations: Round to powers of 2 for easier math
- Work through the math step by step: Show your work to the interviewer
- Validate your assumptions: Check if your numbers make sense
- Consider trade-offs: Use these numbers to justify design decisions
It’s okay to round aggressively during calculations. The goal is to get within the right order of magnitude, not to be perfectly precise.
Additional Resources
