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Numbers and Counting

Numbers and Counting. What you may have forgotten about our number system. 0 1 2 3 4 5 6 7 8 9 10 or 1+0 - One 10 and no units. 11 or One ten and one unit 12 or One ten and two units … 20 or Two tens and no units … 30 or Three tens and no units … 99

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Numbers and Counting

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  1. Numbers and Counting What you may have forgotten about our number system

  2. 0 1 2 3 4 5 6 7 8 9 10 or 1+0 - One 10 and no units 11 or One ten and one unit 12 or One ten and two units … 20 or Two tens and no units … 30 or Three tens and no units … 99 100 or One hundred, no tens and no units Base 10

  3. Base 2 This time, we have only two digits to work with: 0 and 1 0 1 10 or One Two and no Units 11 or One Two and one Unit (2+1=3) 100 or One Four (2^2), no Two and no Units 101 or One Four, no Two, and One Unit (4+1=5) 110 or One Four, One Two and no Units (4+2=6) 111 or One Four, One Two and One Unit (4+2+1=7) 1000 or One Eight (2^3), no Four, no Two and no Unit … 10,000 or One Sixteen (2^4), no Eight, no Four, no Two and no Unit

  4. Binary Coded Decimal (BCD) We group Binary Digits according to Decimal system 1 10 11 100 101 110 111 1000 1001 1 0000 1 2 3 4 5 6 7 8 9 10 • 0001 (11) • 1 0010 • 0011 • 1 0100 • …. • 0000 • ….. • 0001 (21) • …. • 1001 1001 (99) • 0000 0000 (100) • 1 0000 0001 (101)

  5. Hexadecimal – Base 16 Again, we group four Binary Digits 0 0000 • 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 We are out of digits, so we use letters 10 A 11 B 12 C 13 D 14 E • F Now, 10 or One Sixteen and no Units 11 or One Sixteen and one Unit (17 in Base 10) …. 1A or One Sixteen and A (10) units 1B 1C 1D 1E 1F 20 or Two Sixteens and no Units (32 in Base 10)

  6. More Hex 98 99 9A 9B 9C 9D … A9 AA AB … AE AF B0 B1 … F9 FA FB FC FD FE FF 100 or One 256 (16^2), no 16, no Unit When we are talking Hex Numbers, We either add 0x before the number Or we add an “h” at the end of the Number. So, F7B in Hex would be Written as 0xF7B or F7Bh.

  7. Conversion Binary to Hexadecimal: • Group the Binary into sections of four digits each. • Convert the four Binary digits to one digit of Hexadecimal.

  8. 10010101 0101 9 5 Group into fours Convert to Hex Binary to Hex

  9. 110110100001 1010 0001 D A 1 Group into fours Convert to Hex Hex value Binary to Hex, again 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 4 5 6 7 8 9 A B C D E F

  10. EF8 E F 8 1110 1111 1000 Make some room Convert to Binary Hex to Binary 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 4 5 6 7 8 9 A B C D E F

  11. Start with Binary Number 1001 1100 Add up the 1’s: 128 16 8 4 Binary to Decimal 128 64 32 16 | 8 4 2 1 X X X X | X X X X

  12. Binary to Decimal Start with Binary Number 1001 1100 Add up the 1’s: 128 16 8 4 156 in Decimal 128 64 32 16 | 8 4 2 1 X X X X | X X X X

  13. Decimal to Binary • 252 • -128 • 124 • - 64 • 60 • 32 • 28 • -16 • 12 • -8 • 4 • -4 • 0 A lot of subtracting: 252 128 64 32 16 | 8 4 2 1 X X X X | X X X X What 1’s do we have?

  14. Decimal to Binary • 252 • -128 • 124 • - 64 • 60 • 32 • 28 • -16 • 12 • -8 • 4 • -4 • 0 A lot of subtracting: 252 128 64 32 16 | 8 4 2 1 X X X X | X X X X What 1’s do we have? 1111 1100

  15. Decimal to Binary • 89 • -64 • 25 • -16 • 9 • 8 • 1 • -1 • 0 A lot of subtracting: 89 128 64 32 16 | 8 4 2 1 X X X X | X X X X What 1’s do we have?

  16. Decimal to Binary • 89 • -64 • 25 • -16 • 9 • 8 • 1 • -1 • 0 A lot of subtracting: 89 128 64 32 16 | 8 4 2 1 X X X X | X X X X What 1’s do we have? 0101 1001

  17. Grouping Numbers • We start with a bit – one binary digit • A bit is shortened to “b” • Group eight bits together to form a Byte • A Byte is shortened to “B” • Eight bits (one Byte) is the ASCII character set and the foundation of desktop computing • IBM uses a 7-3 code on its big computers

  18. Some ASCII • A capital “A” is (decimal) 65, in Binary it is 0 1 0 0 0 0 0 1 • A capital “B” is 66, in Binary it is 0 1 0 0 0 0 1 0 * A lower case “a” is 97, in Binary it is 0 1 1 0 0 0 0 1 * So the alphabet becomes numbers

  19. More Grouping • Kilo (K) is 1000 in Decimal, 1024 in Binary (2^10) • Mega (M) is one million in Decimal, or 1,048,576 in Binary (2^20) • Giga (G) is one billion in Decimal and slightly larger in Binary (2^30)

  20. How it is Used • Modem speed (limit) is 56K bps – 56,000 bits per second maximum speed For some reason, the FCC limits speed to 54K • RAM capacity is measured in “G” as 2GB Or 2 billion Bytes of memory * Hard disk capacity in G’s: 200GB or 200 Billion Bytes

  21. Bytes • Notice that both RAM and Hard Disk capacity are measured in Bytes. That gets confusing, so let’s spend a moment and work through what each means.

  22. RAM for a moment • RAM = Random Access Memory or Read And Write Memory * Think of RAM as “square somethings” used to measure the size of a desk top. The more RAM, the bigger the desk top and the more piles of things you can make.

  23. Hard Disk Drives • Think of Bytes here as some sort of volume measure. • Hard Disk size is like talking about a file cabinet size – how many Bytes (characters) can it hold (how many drawers). • Storing more information on your Hard Disk does NOT make it run slower!

  24. Brief History of Computing • 1946 ENIAC introduced • Big, took up lots of floor space for vacuum tubes. • Folk legend has it that “bug” was first seen here. • Used to compute where a shell fired from a cannon would land

  25. First Desktop • 1977 Apple introduces the Apple II • Now we had computers on our desks! • By 1980, we had two word processors and VisiCalc (spreadsheet). • Caused a lot of pain in the “IT” department and here is why …..

  26. How Things Worked Computer • You had the computer • You had US • You had THEM US THEM THEM talked to US, who talked to the Computer (using Assembler Language) And US gave THEM the computer output.

  27. Just a Fad • IBM was certain that personal computers would fade out after a couple years. • Just to keep customers happy, they put together a Personal Computer (PC) and stole the name from Apple. • IBM Personal Computer introduced in 1981 with two floppy disk drives.

  28. Side Note • IBM did not want to build an Operating System, so they hired a “kid” who said he had one – his name is Bill Gates. • Bill bought QDOS (Quick and Dirty O S) for $75,000 and then licensed it (NOT sold it) to IBM – hence his first millions. Gary Kidall still shakes his head!

  29. Inside • The core of a computer, or its personality, is in the BIOS – Basic Input\Output System. • So, IBM got lawyers to put up a patent “fence” around the BIOS. BIOS

  30. Some More Numbers • There were about $900 in parts in a PC • It sold for $3500. • Let’s see … 3500 – 900 = 2600 • That number is called PROFIT • Made a lot of people want to build PCs!

  31. In Texas - 1983 • Two very smart guys got together and figured out a BIOS that would get around all the IBM patents – and Compaq computer was born.

  32. More in 1983 • Apple Computer introduces the Lisa – a graphical/mouse computer.

  33. And more 1983 • IBM introduces the XT model, still running at 4.77 MHz but with a hard disk drive (10 MB). * Still $3500. Monitor extra.

  34. 1984 • Apple introduces the Macintosh • IBM introduces the AT model computer with 80286 processor at 6MHz.

  35. 1987 • IBM tries to retake the market by introducing the PS/2 line of computers. Lots of new patents and expensive licensing agreement forms. • Technically superior, but a dud in the marketplace. Required “personality” disks for each expansion card.

  36. 1993 • The Pentium processor introduced. Potential for 32-bit computing in a 16-bit world (DOS).

  37. 1995 • Microsoft launches Windows 95 • Clock speeds reach 266 MHz.

  38. 2000 • Clock speeds reach 1000 MHz, or 1 Gig

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