Data Representation

Data Representation

1. Binary

   • Unsigned
     • 00101011 = 43
       • 0------- => Most Significant Bit (MSB)
       • -------1 => Least Significant Bit (LSB)
       • 2^n -1
         • 8-Bit 0-255 (256 values)
   • Signed
     • Sign and magnitude
       • -43 = 10101011
         • MSB = Signed Bit (1 = - , 0 = +)
         • Rest = positive number
     • 2s compliment
       • binary number (59) l 00111011 one's compliment l 11000100 ................................+1................ two's compliment = 01000101 (-59)
   • Binary Coded Decimal
     • 123 => 1 = 0001, 2 = 0010 , 3 = 0011
     • -37 = 1011 , 0000 , 0011 , 0111
     • Every digit has it's own binary representation
   • Binary Arithmetic
     • Addition
       • 10011101 + ------------------- 11001110 ------------------- 01101011
     • Subtraction
       • 43 +- (20) 43 = 00101011 ..........20 = 00010100 .........-20 = 11101100 ........43-20 = 00101011 + ..................11101100 ................X00010111
         • X = Arithmetic Flow
     • Multiplication
       • 11100 * 101 ------------------- 111100 ------------------- 1000000 ------------------- 1110000 ------------------- 10001100
         • Long Multiplication

2. Representation of chars

   • ASCII (8-bit)
   • UNICODE (16 - bit)
     • ASCII into Unicode (will work) Unicode into ASCII(won't since file is bigger)
   • Unicode used more in general purpose computers but because ASCII is smaller it is used in micro-computers like an Arduino board

3. Representation of Images

   • Raster
     • Stored in pixels
     • Ex: 320 * 200 (8 bit) = 64000 * 1 byte (if 16 -bit *2 bytes)
     • Storage depends on resolution
     • (jpeg, gif, bmp, tiff, png)
       • supports transparancy (kaxex bojod u grizi)
   • Vector
     • stored in shapes
     • Image only resized quality is not restored
     • (wmf , CAD)

4. Representation of Sound

   • Wave for Audio
     • MP3
     • sampling rate directly proportional to quality (24bit - 48k quality)
   • MIDI
     • Stores as a series of instrument and sounds on soundcard
     • Synthesizers, soundcards (Mother and Father to baby Wub)

5. Hexadecimal

   • 0-9 read as integers
     • 10-15 read as A-F
   • Bin- Hex Hex - Bin
     • Kemm taqsamom go 4-bit
   • 23c= 16^2*2 + 16^1 + *3 16^0 * 12 572 -------
   • Dec - Hex
     • 350
       • 21r l E 1 r .l 5 0 r l 1
         • ans = 15E