Digital Audio by the numbers
Understanding what the "BITS" mean for Digital Audio
I spent a quite a number of years working in a cubicle writing low level software and while I have not programmed a digital audio application I did write code that used digital audio modules to create test gear.
I also worked with and managed the very clever engineers who wrote the audio modules soI am very familiar with the meaning of digital numbers and their limitations.
This article is about "bits" and what they mean to audio. On the web, I read a large number of posts where people are trying to get their minds wrapped around these concepts and how 32 bits is different than 16 bits and what is floating point anyway... ? But there never seems to be any good comparative information, in simple terms to help people get to what they are looking for.
The concepts are not beyond the intelligence of an audio engineer, (there's a drummer joke in here somewhere but I am NOT going there!) but they do require some fundamental background to understand. That's what I like to do. Help people with the basics. Then they are prepared to journey off into whatever depth they want to pursue and things will make sense.
Digital Numbers: What are they?
In a word digital numbers are "a code". By “a code” I mean a way to represent something that can be “encoded” so that you can store it easily. And then it can be “decoded” so you can get back what you stored when you need it.
For example, these lines of text that you are reading on your computer screen have nothing to do with the sound humans make to talk but... they are system that you and I both use because we understand the code. I encoded some stuff here and you are now decoding it as you read.
The simplest digital number code system is a switch. It can code for only two conditions. What those two conditions mean is completley up to us. On or OFF. HOT or COLD, UP or DOWN. You get the idea.
Specific Case for Digital Computers
In digital computers the switch means one of two numbers; one and zero. Everybody says that about digital stuff, but unless they are a programmer, they never go much farther. And the dirty little secret is that a lot programmers nowadays don't understand digital number encoding either, because most of the time they just don't need to know.
But what happens if you use more switches? Can you “encode” more numbers? Yes you can! But how many exactly?
OK. Ask yourself “How many combinations of ON and OFF can I make with a number of switches.
(Below 0 means OFF and 1 means ON. Each column is a switch.)
With 1 switch you get 2 possible combinations:
| Switch No. 1 | |
Combination 1 |
Off |
Combination 2 |
On |
With 2 switches, you get 4 possible combinations:
| Switch No. 1 | Switch No. 2 | |
Combination 1 |
Off | Off |
Combination 2 |
Off | On |
Combination 3 |
On |
Off |
Combination 4 |
On | On |
So it turns out that biggest number that you can encode depends on how many switches you have. Simple. To understand how many combinations you get with any number of switches you calculate with a little math.
You just "raise" the number 2 “to the power of" the number of switches that you use. Ok that's a little bit of math but don't freak out. It's easy.
- "2 to power of 2" means 2 x 2 = 4
- "2 to power of 3" means 2 x 2 x 2 = 8
- "2 to power of 4" means 2 x 2 x 2 x 2 = 16
Simple right?
What this is showing is the number of combinations of ON and OFF that you can get with a group of simple switches. If you think of the switches as "BITS" in an audio file things start to come into focus.
What the heck does this mean for Audio? Read on and it will all make sense.