What does it mean that your system is 7-bit, 10-bit or 16-bit?

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

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Alexander Refsum Jensenius is a music researcher and research musician living in Oslo, Norway.

One thought on “What does it mean that your system is 7-bit, 10-bit or 16-bit?”

  1. Several MIDI messages can use two bytes for data representation (MSB and LSB), and then offers a resolution of 2^14 = 16,384.

    In other settings, e.g. digital audio, 32-bit and 64-bit resolution is floating point. e.g. wikipedia would provide more info on how that works.

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