## 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

## Derivatives

A useful thing to do with position data (e.g. from a motion capture system) is to calculate the first and second derivatives. These will give you the velocity and acceleration, respectively. But it doesn’t stop there. In fact, it is possible to continue calculating derivatives of derivatives. Here are the names for the first 10 ones:

• original: position
• velocity (1st)
• acceleration (2nd)
• jerk (3rd)
• snap/jounce (4th)
• crackle (5th)
• pop (6th)
• Lock (7th)
• Drop (8th)
• Shot (9th)
• Put (10th)

Whether these are useful or not is another question…