In music technology we often talk about n-bit systems. For example, the MIDI protocol is based on a 7-bit scheme, many sensor interfaces use 10-bit resolution for their sensor readings, and sound cards typically record in 16-bit, or even 32-bit. But even though we talk about these things every day, I am often surprised by how many people don’t really know what 7-bit actually means, and that a 32-bit system is not “double” as good as a 16-bit system.
I googled around a little, but couldn’t find a plain and easy table explaining the concept, so here it is, a table showing how many values/combinations you can have in systems with various types of bit-rate:
| Bits | Exponent | Calculation | # Values |
| 2-bit | 2^2 | 2×2 | = 4 |
| 3-bit | 2^3 | 2x2x2 | = 8 |
| 4-bit | 2^4 | 2x2x2x2 | = 16 |
| 5-bit | 2^5 | 2x2x2x2x2 | = 32 |
| 6-bit | 2^6 | 2x2x2x2x2x2 | = 64 |
| 7-bit | 2^7 | 2x2x2x2x2x2x2 | = 128 |
| 8-bit | 2^8 | 2x2x2x2x2x2x2x2 | = 256 |
| 9-bit | 2^9 | 2x2x2x2x2x2x2x2x2 | = 512 |
| 10-bit | 2^10 | 2x2x2x2x2x2x2x2x2x2 | = 1024 |
| 11-bit | 2^11 | 2x2x2x2x2x2x2x2x2x2… | = 2048 |
| 12-bit | 2^12 | 2x2x2x2x2x2x2x2x2x2… | = 4096 |
| 16-bit | 2^16 | 2x2x2x2x2x2x2x2x2x2… | = 65 536 |
| 24-bit | 2^24 | 2x2x2x2x2x2x2x2x2x2… | = 16 777 216 |
| 32-bit | 2^32 | 2x2x2x2x2x2x2x2x2x2… | = 4 294 967 296 |