Welcome to this video on binary and digital data.

A good understanding of digital audio theory is essential for home and project studio owners. Many decisions taken during audio production depend on it. The first step is to ensure we understand the primary underlying concepts of a digital system, digital base 2 binary counting systems. These concepts inform all aspects of digital audio theory.

Caption - Decimal - base 10

As we all know, decimal can represent a range of 10 values in a single symbol, from 0 to 9. We might say that these symbols are the alphabet of decimal and that they can be combined to form bigger numbers which are decimal's equivalent of words.

When we read a large decimal word, such as one thousand and twenty four, we understand it because we have been educated to know what value each of the individual numbers represents and how they are organised.

Caption - Binary base 2

Binary is the base 2 counting system on which all digital information and software is based, including ..

operating systems

applications

.. and data, including digital audio

Complex strings of 1's and 0's are combined to create the files which comprise the digital systems we use.

Caption - The Bit - the digital alphabet

Binary is the logical choice of counting system for digital computers because at the physical level of machine code, including electrical signals and transistors, computers are limited in how they can represent information. Digital signals only have 2 states, on and off and can therefore only represent one of 2 values in a single digit .. 0 and 1.

A single digit of digital information is known as a bit. The bit is the alphabet of binary.

Caption - Bytes - the digital word

A bit on its own is not much use, so multiple bits are combined to form digital words known as bytes. Early computers used an arrangement of 8-bit bytes, and this system has endured. The following are a few examples showing a decimal number and its equivalent byte...

Although this arrangement means that a single digit decimal number, such as 5, requires 8 digits, 0 0 0 0 0 1 0 1, when represented in a binary byte, there are huge advantages, not least of which is the ability to process and transmit digital signals at the speed of light and for binary data to be represented in many different physical forms.

A single 8-bit binary byte has a minimum decimal value of 0, which is eight 0's in a row, and maximum value of 255, which is eight 1's in a row. It can therefore represent 256 different decimal values between 0 and 255.

Caption - Pulse code modulation

In order to represent a sequence of bits and bytes, a digital signal must modulate in a process known as Pulse Code Modulation, or PCM for short. Pulse Code Modulation produces a pulse wave signal which rises and falls to represent the 1's and 0's.

Pulse code modulation is at the heart of digital audio signals. The term Pulse Code Modulation is often used in the context of digital signals themselves and the process by which they are created, such as analogue to digital conversion.

Caption - Digital "sentences"

Like words in the English language, individual bytes are of limited use, but when combined into 'sentences' they become expressive and powerful.

00110111 11100011 10101011 00000111 01111110 01010000 01111110 10000001 00000001 11111011

These sentences can be used to form different types of software and data including ..

applications

plug-ins

operating system components

digital audio files

DAW project files

.. and web pages

 

Caption - Word length

Combining bytes into sentences allows complex software components to be created, however, unlike decimal where individual numbers in a system can be any number of digits long, the bytes that comprise a digital file are almost always restricted to a fixed length.

For example, the bytes in a GIF image file are always a fixed length, with each byte representing the position and colour of a single pixel. GIFs have a maximum word length of 8-bits and a minimum of 1-bit which is black and white. There is a good reason for this limitation because it helps keep the overall file size small and therefore quick to transfer over a network.

However, for other types of software and data, 8-bit word length is inadequate. Therefore 8-bit bytes are combined to form longer word lengths. For example, the bytes in a red book CD quality audio file are 16 bits long. In this example we would say that the CD file format uses a 16-bit word length.

As word length increases the range of decimal values that they can represented increases exponentially. For example ..

A single 16 bit binary byte has a minimum decimal value of 0, which is sixteen 0's in a row, and maximum value of 65,535 which is sixteen 1's. It can therefore represent 65,536 different decimal values between 0 and 65,535.

16-bit byte	Decimal (equivalent)
0000000000000000	0
0000000000000001	1
etc	etc
1111111111111110	65,534
1111111111111111	65,535

 

 

A single 24 bit binary byte has a minimum decimal value of 0, which is twenty four 0's in a row, and maximum value of 16,777,215 which is twenty four 1's in a row. It can therefore represent 16,777,216 different decimal values between 0 and 16,777,215.

24-bit byte	Decimal (equivalent)
000000000000000000000000	0
000000000000000000000001	1
etc	etc
111111111111111111111110	16,777,214
111111111111111111111111	16,777,215

 

In a nutshell, greater word lengths allow for a greater degree of quality and accuracy, but require more storage space and greater computational power.

Caption - Thanks for watching

The script for this video, with accompanying images, can be found at projectstudiohandbook.com 

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