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 2x2 = 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