# Binary Numbers

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Introduction to Computer Music: Volume One

Modules 1. Overview 2. Binary Numbers 3. Sampling 4. Nyquist Theorum 5. Sample Rates 6. Quanitization 7. DACs 8. Audio File Formats 9. References Chapters Table of Contents 1. Acoustics 2. Studio Gear

Chapter Five: Digital Audio 2. Binary numbers, bits and bytes Binary numbers A rudimentary knowledge of how binary numbers work is required in order to understand the mechanism of digital audio. A good way to start is with decimal numbers, which are much more familiar to most of us. Each "place" of a decimal number is filled by a digit. Our decimal system is called base-10, meaning that each digit can express 10 values, ranging from zero to nine. To express a quantity greater than 9, we need an additional digit or digits (we are ignoring decimals for the time being). Each place of a base-10 number represents a power of 10 (with 10^0=0-9), so 1's, 10's, 100's, etc. Binary numbers developed as a symbolic representation of computer circuits, which can be thought of as a series of switches that are either on or off. It seemed logical to use our first two familiar symbols, 0 and 1 to represent these two states (you might think 0=off and 1=on, but in some cases, you would be wrong). A single-place binary number is called a bit, which is short for "Binary digIT." Binary numbers are base-2, with each place representing the powers of two (as opposed to ten in our decimal system). The places for a binary number from right to left are 1's, 2's, 4's, 8's, 16's, 32's, etc. or 20, 21, 22, 23, 24, 25, 26, etc. which add up cumulatively if there is a '1' in that particular place.

3. MIDI

powers of 2

23

22

21

20

4. Synthesis

equivalent decimal values

8's

4's

2's

1's

sample 4-bit binary number

1

0

1

1

how to solve

8 +

0 +

2 +

1 =

5. Digital Audio Appendices

11 (decimal)

Below is a chart of some equivalent decimal and binary values: 0 = 0

4 = 100

8 = 1000

12 = 1100

1 = 1

5 = 101

9 = 1001

13 = 1101

2 = 10

6 = 110

10 = 1010

14 = 1110

3 = 11

7 = 111

11 = 1011

15 = 1111

For a more extensive printable chart, click here. 1 | 2 | 3

| Jacobs School of Music | Center for Electronic and Computer Music | Contact Us | ©2017-18 Prof. Jeffrey Hass

## Binary Numbers

CECM Home | People | Degrees | Courses | Facilities | Documents | Links Introduction to Computer Music: Volume One Modules 1. Overview 2. Binary Nu...

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