Computer OrganizationHigh Level View Of A ComputerGetting Data InSlide 4Getting Data OutSlide 6Unit of StorageHow Data Is StoredHow Data Is StoredBinary NumbersConverting Binary to Base 10Converting Base 10 to BinarySlide 13Other common number representations__________ NumbersRepresenting ________ Numbers_____________________________________________Real (____________) numbersLimitations of Finite Data EncodingsLimitations of Finite Data ExchangeSlide 22J. Michael MooreComputer OrganizationCPSC 110J. Michael MooreHigh Level View Of A ComputerProcessorInput OutputMemoryStorageJ. Michael MooreGetting Data InInputOthers?J. Michael MooreProcessorInput OutputMemoryStorageJ. Michael MooreGetting Data OutOutputOthers?J. Michael MooreProcessorInput OutputMemoryStorageJ. Michael MooreUnit of Storage•___–_____ ______–Smallest unitof measurementMemoryStorageTwo possiblevalueson offORJ. Michael MooreHow Data Is Stored•___: a group of 8 bits; 28=256 possibilities–00000000, 00000001, 00000010, 00000011, … , 11111111•___________: long sequence of locations, each large enough to hold one byte, numbered 0, 1, 2, 3, …•___________: The number of the locationJ. Michael MooreHow Data Is Stored•Contents of a location can change–e.g. 01011010 can become 11100001•Use consecutive locations to store longer sequences–e.g. 4 bytes = 1 word1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 003...bytes0 1 2bitsJ. Michael MooreBinary Numbers•Base Ten Numbers (Integers)–characters•0 1 2 3 4 5 6 7 8 9–5401 is 5x103 + 4x102 + 0x101 + 1x100•Binary numbers are the same–characters•0 1–1011 is 1x23 + 0x22 + 1x21 + 1x20J. Michael MooreConverting Binary to Base 10•23 = 8•22 = 4•21 = 2•20 = 11. 10012 = ____10 =2. 1x23 + 0x22 + 0x21+ 1x20 =3. 1x8 + 0x4 + 0x2 + 1x1 =4. 8 + 0 + 0 + 1 =5. 910•01102 = ____10 (Try yourself)•01102 = 610J. Michael MooreConverting Base 10 to Binary•28 = 256•27 = 128•26 = 64•25 = 32•24 = 16•23 = 8•22 = 4•21 = 2•20 = 1•38810 = ____2 2827262425222320211 1 10 00 0 00•388 - 256 (28) = 132•132 - 128 (27) = 4•4 - 4 (22) = 0J. Michael MooreConverting Base 10 to Binary•38810 = ____2 •38810 / 2 = 19410 Remainder 0•19410 / 2 = 9710 Remainder 0•9710 / 2 = 4810 Remainder 1•4810 / 2 = 2410 Remainder 0•2410 / 2 = 1210 Remainder 0•1210 / 2 = 610 Remainder 0•610 / 2 = 310 Remainder 0•310 / 2 = 110 Remainder 1•110 / 2 = 010 Remainder 12827262425222320211 1 10 00 0 00J. Michael MooreOther common number representations•_____________ Numbers–characters•0 1 2 3 4 5 6 7 8–7820 is 7x83 + 8x82 + 2x81 + 0x80•_____________ Numbers–characters•0 1 2 3 4 5 6 7 8 9 A B C D E F–2FD6 is 2x163 + Fx162 + Dx161 + 6x160J. Michael Moore__________ Numbers•Can we store a __________ sign?•What can we do?–Use a ____•Most common is ____________________J. Michael MooreRepresenting ________ Numbers•____________________________–flip all the bits•change 0 to 1 and 1 to zero–add 1–if the leftmost bit is __, the number is __ or _______________–if the leftmost bit is __, the number is _______________J. Michael Moore______________________•What is -9?–9 is 00001001 in binary–flip the bits → 11110110–add 1 → 11110111•Addition and Subtraction are easy–always additionJ. Michael Moore_______________________•Addition–13 - 9 = 4–13 + (-9) = 4–00001101 + 11110111 = ?00 100 0 0 11110101 1 1 11 1 11011 1 10000 4=1This bit is lostBut that doesn’t matter since we get the correct answer anywayJ. Michael MooreReal (____________) numbers•Break the bits used into parts0110101000000011________ ________Sign bitsJ. Michael MooreLimitations of Finite Data Encodings•__________ - number is too large–suppose 1 byte stores integers in base 2, from 0 (00000000) to 255 (11111111) (note: this is not ___________________ although it would have the same problem)–if the byte holds 255, then adding 1 to it results in __, not _____J. Michael MooreLimitations of Finite Data Exchange•___________ Error–Insufficient ___________ (size of word)•ex. Try to store 1/8, which is 0.001 in binary, with only two bits–______________ expansions in current base•ex. Try to store 1/3 in base 10, which is 0.3333…–______________ expansions in every base•ex. Irrational numbers such as J. Michael MooreProcessorInput
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