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Bits and BytesCOMP 102, lecture 2
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What are bits and bytes
bit (b): 0 or 1
byte (B): 8 b (28 = 256 possibilities) 00000000 00000001 00000010 00000011 00000100 00000101 00000110 00000111 00001000 00001001 00001010 00001011 ... 11111100 11111101 11111110 11111111 numerical equivalents: 0,1,2,...,255
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Decimal vs Binary
Decimal numbers:d5d4d3d2d1d0 = d5x105+d4x104+d3x103+d2x102+d1x101+d0x100 154283 = 100 000+50 000+4 000+200+80+3
Binary numbers:b5b4b3b2b1b0 = b5x25+b4x24+b3x23+b2x22+b1x21+b0x20
101001 = (1x32)+(0x16)+(1x8)+(0x4)+(0x2)+(1x1) = 41 (decimal)
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Decimal vs Binary
Example:write the decimal number 154283 in binary
powers of 2:1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, ...
154283 - 131072 = 23211 23211 - 16384 = 68276827 - 4096 = 2731 2731 - 2048 = 683 683 - 512 = 171 171 - 128 = 43 43 - 32 = 11 11 - 8 = 3 3 - 2 = 1 1 - 1 = 0
15428310 = 10 0101 1010 1010 10112
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Binary numbers.
Integer formats32 bits, unsigned Integers : 0 .. 4 294 967 295 32 bits, signed Integers : −2 147 483 648 .. +2 147 483 647
Floating Point format32 bits, signed, Floating Point : exponent : -126 .. 127fraction = 0 to 1-2-23 (1.fraction)
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Integer formats
32 bits, unsigned Integers : 0 .. 4 294 967 295 00000000 00000000 00000000 00000000(0) 00000000 00000000 00000000 00000001(1) 00000000 00000000 00000000 00000010(2) ... 11111111 11111111 11111111 11111110(4 294 967 294) 11111111 11111111 11111111 11111111(4 294 967 295)
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Integer formats
32 bits, signed, Integers : −2 147 483 648 .. +2 147 483 647 00000000 00000000 00000000 00000000(0) 00000000 00000000 00000000 00000001 00000000 00000000 00000000 00000010 ... 01111111 11111111 11111111 11111111(+2 147 483 647)10000000 00000000 00000000 00000000(-2 147 483 648)10000000 00000000 00000000 00000001(-2 147 483 647)... 11111111 11111111 11111111 11111110(-2) 11111111 11111111 11111111 11111111(-1) for any n>0, -n = (n-1) ⊕ 1111111 ... 1111
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Floating Point format
32 bits, signed, Floating Point : exponent : -126 .. 127 (stored as 1 .. 254)(special exponents / = -127 : number = 0 / = 128 : number = ∞)fraction = 0 .. 1-2-23
number = ± 1.fraction x 2(exponent-127)
0 01111111 00000000000000000000000 = +1.0 x 20 1 01111111 00000000000000000000000 = -1.0 x 20 0 11111111 00000000000000000000000 = ∞ 1 01010101 10000000000000000000000 = -1.5 x 2-42 0 01111100 01000000000000000000000 = +1.25 x 2-3 = +0.15625
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Computer Jargon
measuring space in bits (b) or bytes (B)
measuring transfer rates in bits per second (b/s) or (bps)
measuring speed in Hertz (Hz)
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Metric System
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Metric System
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“Binary” metric system
210 = 1024 ≈ 1000 = 103
1 kB = 1024 B
1 MB = 1024 kB = 1 048 576 B
1 GB = 1024 MB = 1 073 741 824 B
1 TB = 1024 GB = 1 099 511 627 776 B
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STORAGE DEVICES
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Current devices
CD 700 MB
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Current devices
DVD
single layer 4,7 GB and double layer 8,3 GB
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Current devices
Blu-ray
single layer 25 GB and double layer 50 GB
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Current devices
Flash memory: 32 GB cheap, 128 GB expensive
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Current devices
RAM (computer): 8 GB cheap, 16 GB expensive
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Current devices
Hard Disk: 2 TB cheap, 4 TB expensive
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Current devices
Solid State Drive: 256 MB cheap, 1 TB expensive
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Connection types
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Current connectivity
telephone Modem (V.92)
download speeds up to 56 kbit/s≈ DVD / 12 daysupload speeds up to 48 kbit/s
fax (V.34)
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Current connectivity
telephone Modem (V.92)
download (to here) speeds up to 56 kbit/s= download speeds up to 201600 kbit/hour (3600s/hour)≈ download speeds up to 4,838 Gbit/day (24hour/day)≈ download speeds up to 605 MB/day (8 b/B)≈ DVD / 12 days
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Current connectivity
Internet connections (cable or fibre-optics)
videotron 200 Mbps≈ DVD / 3 min
Bell/Fibe 175 Mbps≈ DVD / 4 min
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Current connectivity
Internet connections (wireless)
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Current connectivity