1. Computer Some basic concepts

2. Binary number Why binary? Look at a decimal number: 3511 Look at a binary number: 1011 counting decimal0123456789 binary011011100

3. Binary number Maximum possible  8 bits:  40 bits:  N bits: What is the number after 10111?

4. Hexadecimal Decimal: base 10 Binary: base 2 Hexadecimal: base 16 But works the same way Translate F1C: Where do you see it?

5. decimal binary hexadecimal 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F

6. Size 1 byte = 8 bits 1KB = 2^10 bytes 1MB = 2^20 bytes 1GB = 2^30 bytes 1TB = 2^40 bytes

7. ASCII ASCII (American Standard Code for Information Interchange) How to represent a keyboard character as a number? Assigns a unique number (0-127) to each keyboard character. Examples:  a - 97  A to Z: 65-90  a to z: 97-122  0 to 9: 48-57

8. Unicode 127 is not enough Other languages Same principle More characters

9. Digitizing the world

10. Example: Digitizing Sound An object creates sound by vibrating in a medium such as air  Vibrations push the air  Pressure waves emanate from the object and vibrate our eardrums  The force, or intensity of the push determines the volume  The frequency (number of waves per second) is the pitch

12. Analog to Digital To convert continuous information, convert it to bits From zero line on graph, record with binary number the amount by which the wave is above or below it (positive or negative sound pressure) At what points do we measure? We can't record every position of the wave

13. Sampling Take measurements at regular intervals Number of samples in a second is the sampling rate  The faster the rate, the more accurate the recording

14. How Fast to Sample? Sampling rate should be related to the wave's frequency  Too slow rate could allow waves to fit between the samples; we'd miss segments of sound  Guideline is Nyquist Rule: Sampling rate must be at least twice as fast as the fastest frequency Human perception can hear sound up to 20,000 Hz, so 40,000 Hz sampling rate is enough. Standard for digital audio is 44,100 Hz

15. How Many Bits per Sample? How accurate must the samples be?  Bits must represent both positive and negative values  The more bits, the more accurate the measurement  The digital representation of audio CDs uses 16 bits (records 65,536 levels, half above and half below the zero line)

17. How large is one-minute music? One-minute digital audio?  60 seconds  44,100 samples  16 bits each  Times 2 for stereo  60*44,100*2(Bytes)*2=10.5 MB! An hour is 635MB!

18. ADC, DAC Digitizing Process:  Sound is picked up by a microphone (called a transducer)  The signal is fed into an analog-to-digital converter (ADC), which samples it at regular intervals and outputs binary numbers to memory  To play the sound, the process is reversed Numbers are read from memory into digital-to-analog converter (DAC), which creates an electrical wave by filling in between the digital values Electrical signal is output to speaker, which converts it to a sound wave

20. Advantages of Digital Sound (MP3) Compression  One computation is to compress the digital audio (reduce number of bits needed)  Remove waves that are outside range of human hearing  Teen-only ringtone  MP3 usually gets a compression rate of 10:1 Lower bandwidth requirements, popular for Internet transmission Reproducing the Sound Recording  Bit file can be copied without losing any information  Original and copy are exactly the same  Vinyl recording is analog, it wears out.  Easy “transportation” We can compute the representation  Enhance, manipulate  Synthetic voice