CSC103 How Computers Work

Notes3

1. Digitization high-level:
   • thing → numbers
   • numbers → binary
   • binary → bits
   • bits → physical bits
2. Binary notation
   • Abstract number (in Platonic heaven): e.g., twenty seven
   • Notated in many "representation systems": unary, binary, octal, decimal, hexidecimal
   • Unique representation
   • unary: 111111111111111111111111111₁
   • binary: 11011₂
   • octal: 33₈
   • decimal: 27₁₀
   • hexadecimal: 1B₁₆
   • Babylonian: : base 60
3. Conversion
   • Conversion: binary to decimal: multiplication
     • 27₁₀ → 27₁₀
     • 11011₂ → 27₁₀
       • 16+8+0+2+1 = 27
   • Conversion: decimal to binary: division
     • two hundred fifty six → 256₁₀
       • 256/10 = 25 remainder of 6
       • 25/10 = 2 reminder of 5
       • 2/10 =0 remainder of 2
     • twenty seven →11011₂
       • 27/2 = 13 remainder of 1
       • 13/2 = 6 remainder of 1
       • 6/2 = 3 remainder of 0
       • 3/2 = 1 remainder of 1
       • 1/2 = 0 remainder of 1
     • divide by base, note remainder
     • get digits least-significant to most-significant
     • check by converting in other direction
4. Bits
   • Binary Digit
   • Some physical two-state device represents a bit:
   • 0/1, False/True→Off/On, low voltage/ high voltage, S/N, pit/no pit,...
   • Represent any number via the bits of the binary representation of that number
   • Bits & Bytes: abbreviated b and B
5. Bits & Bytes: b and B
   • K, M, G, T
   • Memory size:
     • 640MB [CD], 10GB [DVD]: Bytes
   • Transmission speed: bits
     • 56 Kbps, 1Mbps, etc.
6. Representing Characters (Letters)
   • ASCII (1967); Table
   • !=33,"=34,A=65..Z=90, a=97..z=122,..,~=126
   • Unicode
   • 1 Byte for ASCII chars + up to 4 bytes for others.
7. Representing images
   • 24 bits = 3 bytes per pixel, 8 bits each RGB.
   • 8 bits = 256 shades/intensities of color
   • Usually represented as a hex triplet: #000000, #FFFFFF, etc.
   • Web colors
   • JPEG, GIF, PNG, etc.
8. Representing Sound
   • sample signal strength thousands of times per second, store strength in binary number
   • 44,000 samples per second, each 16 bits.
   • WAV, AIFF, RA, MP3, etc.
9. Digitization: representing something by discrete samples
   • Big idea: essentially anything can be digitized
   • (Some philosophical controversy over this)
   • Need to convert back again: representation → image, sound, etc.