Sound for Interaction class 9
- Audio Effects Presentations
- Intro to digital theory
Contents
Digital Theory
Word of the Day Analog How stuff works - How Analog and Digital Recording Works
Analog vs. Digital the arguments in a nutshell
Analog | Digital Good |
---|---|
Infinite dynamic quantization (infinite resolution) | Quantization error fix - more bit depth/oversampling |
Good? - The warming effects 'we're used' to from tape compression. | Good?-'Perfect' reproduction of high frequencies - 'soundz harsh fix - 'using warm-sounding mikes and preamps (tubes)' |
Bad - Tape noise and generation loss | Good - 'no generation loss' |
Bad - 'Cheap recordings sound cheap' | Good - 'cheap recordings sound good but digital' |
* 'anything in quotes is what I like to call an opinion
Other Opinions
analog winner http://www.segall.com/atr.html
analog winner http://www.digido.com/analog_versus_digital.html
comparison http://www.outersound.com/osu/recording/
ana-dig.html Number Systems
Hexadecimal Base 16 | Decimal Base 10 | Octal Base 8 | Binary Base 2 |
---|---|---|---|
0 | 0 | 0 | 0000 |
1 | 1 | 1 | 0001 |
2 | 2 | 2 | 0010 |
3 | 3 | 3 | 0011 |
4 | 4 | 4 | 0100 |
5 | 5 | 5 | 0101 |
6 | 6 | 6 | 0110 |
7 | 7 | 7 | 0111 |
8 | 8 | 10 | 1000 |
9 | 9 | 11 | 1001 |
A | 10 | 12 | 1010 |
B | 11 | 13 | 1011 |
C | 12 | 14 | 1100 |
D | 13 | 15 | 1101 |
E | 14 | 16 | 1110 |
F | 15 | 17 | 1111 |
Binary Numbers
As Humans we use a 10 base numbering system. For machines this numbering system is impractical.
Gottfried Willheml von Leibnitz devised the binary number system in 1679
Converting Binary Numbers
Binary->Decimal
110102 = (1 * 24) + (1 * 23) + (0 * 22) + (1 * 21) + (0 * 20) = 1610 + 810 + 0 + 210 + 0 = 2610
Dividing by two
integer | remainder | binary # |
---|---|---|
26 | ||
26/2 | 0 | 0 |
13/2 | 1 | 1 0 |
6/2 | 0 | 0 1 0 |
3/2 | 1 | 1 0 1 0 |
1/2 | 1 | 1 1 0 1 0 |
0/2 | that's it kids |
for more info see Dr. Dave's Class readings (i believe it's in week 2)Daves text
Base2
Each new bit doubles the number of intervals.
20 | =1 | monochrome, often black and white |
21 | =2 | |
22 | =4 | |
23 | =8 | Most early color Unix workstations, VGA at low resolution, Super VGA, AGA http://en.wikipedia.org/wiki/Web_colors#Web-safe_colors |
24 | =16 | |
25 | =32 | |
26 | =64 | |
27 | =128 | |
28 | =256 | |
29 | =512 | |
210 | =1024 | |
2 11 | =2048 | |
212 | =4096 | |
213 | =8192 | |
214 | =16384 | |
215 | =32768 | |
216 | =65536 | "thousands of colors" on Macintosh |
220 | =1048576 | |
224 | =16777216 | Truecolor or "millions of colors" on Macintosh systems |
232 | = 4,294,967,295 | refers to 24-bit color (Truecolor) with an additional 8 bits |
264 | = 18,446,744,073,709,551,616 | = 16 exabytes. That's more than 18 billion billion bytes. |
Large Bit Names
Name | Abbr. | Size |
---|---|---|
Kilo | K | 2^10 = 1,024 |
Mega | M | 2^20 = 1,048,576 |
Giga | G | 2^30 = 1,073,741,824 |
Tera | T | 2^40 = 1,099,511,627,776 |
Peta | P | 2^50 = 1,125,899,906,842,624 |
Exa | E | 2^60 = 1,152,921,504,606,846,976 |
Zetta | Z | 2^70 = 1,180,591,620,717,411,303,424 |
Yotta | Y | 2^80 = 1,208,925,819,614,629,174,706,176 |
Color Depth
http://en.wikipedia.org/wiki/Color_depth
Large Bit Names
Name | Abbr. | Size | Kilo | K | 2^10 = 1,024 |
---|---|---|---|---|---|
Mega | M | 2^20 = 1,048,576 | |||
Giga | G | 2^30 = 1,073,741,824 | |||
Tera | T | 2^40 = 1,099,511,627,776 | |||
Peta | P | 2^50 = 1,125,899,906,842,624 | |||
Exa | E | 2^60 = 1,152,921,504,606,846,976 | |||
Zetta | Z | 2^70 = 1,180,591,620,717,411,303,424 | |||
Yotta | Y | 2^80 = 1,208,925,819,614,629,174,706,176 |
Binary Math
OPTIONAL
Binary Math http://www.ibiblio.org/obp/electricCircuits/Digital/DIGI_2.html What can one byte (8 bits) store? 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 1 1 1 1 1 1 1 1 128 64 32 16 8 4 2 1 128+64+32+16+8+4+2+1 = 255
What about negative numbers? Signed Magnitude
Use the first bit as the equivalent of a +/- sign.
http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary.html 510 in 8 bit binary 00000101
-510 in 8 bit binary Signed Magnitude 10000101 (make sure that the circuit knows you are using singed magnitude otherwise this could be interpreted as 113)
Now what can one byte (8 bits) store?
+/- 2^6 2^5 2^4 2^3 2^2 2^1 2^0
0 1 1 1 1 1 1 1
+ 64 32 16 8 4 2 1
64+32+16+8+4+2+1 = 127
or
+/- 2^6 2^5 2^4 2^3 2^2 2^1 2^0
1 1 1 1 1 1 1 1
- 64 32 16 8 4 2 1
-64+32+16+8+4+2+1 = -127
One's Compliment
One's Compliment uses regular binary numbers to represent positive numbers. To make that number negative you just flip all the bits from 1 to 0 or 0 to 1. 510 in 8 bit binary 00000101
-510 in 8 bit binary One's Compliment 11111010
Two's Compliment
Same as One's Compliment bit add one to negative numbers 510 in 8 bit binary 00000101
-510 in 8 bit binary Two's Compliment 11111011
To figure out the sign of the answer we must check the MSB (most significant bit).If MSB is 0 number is positive, interpret normally If MSB is 1 number is negative
* complement all bits * add 1 * interpret as negative number