Audio Bit Depth: Part 1

Audio Bit Depth. That old chestnut! It took me a while to really wrap my head around what it actually is. For a long time I seemed to grasp the almost cliché explanations like “It’s the dynamic range of audio”, or “one bit equals 6dB”, or the vague term “resolution”. While they aren’t entirely incorrect statements, they are easily misunderstood. Despite growing up with computers and receiving a university education in music composition and sound production, I still didn’t join the dots (pun intended) until the first few lectures of a computer science degree. Who knows. It could have entirely been my fault. Perhaps I missed a digital audio lecture containing a pivotal piece of information or something. Or perhaps everyone was simply in the same boat… clutching the simplest of explanations.

audio bit depth
An analogue rotary counter

So… what I have learnt? The first step and the subject of this part of the article is understanding the basics of bits and binary. It is impossible to gain a decent understanding of what bit depth is without tackling what a bit is first. The term ‘bit’ is a portmanteau (contraction) of the phrase Binary Digit. An 0 or a 1. From these two simple characters the greater system of binary is built.

So what is binary? 0’s and 1’s? On’s and off’s? Binary is actually a number system. A binary digit is to binary, what a digit is to our decimal number system. We use the decimal system in our day-to-day lives to count pretty well everything and anything. The decimal system is a base-10 counting system named from the latin term Decimus, meaning tenth. Everything about it revolves around ten. We use ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) in patterns and multiples of ten to create a counting system that allows us to represent pretty much anything mathematically.

One of the easiest ways I have found to understand how counting systems work is to imagine an old analogue rotary counter like those found in old car odometers, or in old mains water meters, or like the handheld click-counter that a venue bouncer might use to count the number of people entering a nightclub. There is one wheel for units, another for tens, another wheel hundreds, etc. Each wheel has 0 through 9 on it and they spin in sequence as it counts. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9… then the pattern repeats and the wheel to the left increments by 1. 10, 11, 12, 13, 14, 15, 16, 17, 18, 19… and so on. Each wheel only spins once all the wheels to the right of it have been through all the possible number combinations. The only way you get a reading of ’10’ is if the wheel on the right has spun through 0 to 9. The only way you get to 100 is if the units and tens wheels both make it to 99.

Binary works on the same fundamental premise, but instead of being a base-10 counting system it is a base-2 counting system. Binarius being latin for “consisting of two”. As such, it uses just two symbols – 0 and 1 (binary digits), and it revolves around multiples of two. If we were to construct an analogue rotary counter that counts in binary each wheel would have just 0 and 1 on them. Counting – 0, 1 then the next wheel would increment by 1. 10, 11, then the wheel to the left would increment by one. 100, 101, 110, 111, and so on.

One of the beautiful things about number systems is that they are easily translatable backwards and forwards between each other. Twelve eggs in your basket is always twelve eggs regardless of the number system you use to represent it. In decimal it is ’12’. In binary it is ‘1100’. Other common number systems out there include the Octal number system. It is a base-8 system using 8 symbols (0 through 7). In octal, twelve would be expressed as ’14’! Counting through the octal – 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14.  Hexadecimal is a base-16 counting system that uses 16 different cymbals – 0 through 9, and then A through to F to represent 10 through to 15. Yep, that’s right. Letters. In a counting system. Twelve eggs in your basket would be expressed as ‘C’ eggs in your basket in hexadecimal. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C.

It can be a tricky thing to wrap your head around simply because we are so programmed to use the decimal system. I personally found it easier to understand once I stopped trying to read the numbers and just concentrated on the symbols and the way they are used in patterns. It is this fundamental pattern of revolving symbols that is shared between the plethora of different number systems out there. Below is a simple 16 value animated counting sequence that shows both the binary and decimal counting up to 15. Zero is a number, and an important one at that!

4-Bit Binary to Decimal Conversion
4-Bit Binary to Decimal Conversion

Hopefully that explanation has resulted in a bit of a clearer explanation on what binary actually is. (So punny!). In the next article on bit depth we will be covering how bits and binary apply in the wider concept of audio bit depth. As always, we welcome any comments, corrections and ideas regarding this article! Please feel free to comment!

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