And Bits and Bytes Everything in the computer is stored as: 1,024 Bytes = Kilobyte (KB) 1,024 KB = Megabyte (MB) 1,204 MB = Gigabyte (GB) 1,204 GB = Terabyte (TB) 1,204 TB = Petabyte (PB) 1,024 PB = Exabyte (EB) 1,024 EB = Zettabyte (ZB) 1,024 ZB = Yottabyte (YB) 0 1 8 bits (Binary Digits) = 1 Byte 1,024 1,048,576 1,073,741,824 1,099,511,627,776 1,125,899,906,842,624 1,152,921,504,606,846,976 1,180,591,620,717,411,303,424 1,208,925,819,614,629,174,706,176 A TRILLION x TRILLION … Wow, that’s a Yotta bytes!!!
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 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129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 132 132 132 132 132 132 132 132 132 132 133 133 133 133 133 133 133 133 133 133 133 133 133 133 133 133 133 133 134 134 134 134 134 134 134 134 134 134 134 134 134 134 134 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 135 135 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 136 137 137 137 137 137 137 137 137 137 137 137 137 137 137 138 138 138 138 138 138 138 138 138 138 138 138 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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Or • 402,387,260,077,093,773,543,702,433,923,003,985,719,374,864,210,714,632,543,799,910,429,938,512,398,629,020,592,044,208,486,969,404,800,479,988,61 0,197,196,058,631,666,872,994,808,558,901,323,829,669,944,590,997,424,504,087,073,759,918,823,627,727,188,732,519,779,505,950,995,276,120,874,975, 462,497,043,601,418,278,094,646,496,291,056,393,887,437,886,487,337,119,181,045,825,783,647,849,977,012,476,632,889,835,955,735,432,513,185,323,95 8,463,075,557,409,114,262,417,474,349,347,553,428,646,576,611,667,797,396,668,820,291,207,379,143,853,719,588,249,808,126,867,838,374,559,731,746, 136,085,379,534,524,221,586,593,201,928,090,878,297,308,431,392,844,403,281,231,558,611,036,976,801,357,304,216,168,747,609,675,871,348,312,025,47 8,589,320,767,169,132,448,426,236,131,412,508,780,208,000,261,683,151,027,341,827,977,704,784,635,868,170,164,365,024,153,691,398,281,264,810,213, 092,761,244,896,359,928,705,114,964,975,419,909,342,221,566,832,572,080,821,333,186,116,811,553,615,836,546,984,046,708,975,602,900,950,537,616,47 5,847,728,421,889,679,646,244,945,160,765,353,408,198,901,385,442,487,984,959,953,319,101,723,355,556,602,139,450,399,736,280,750,137,837,615,307, 127,761,926,849,034,352,625,200,015,888,535,147,331,611,702,103,968,175,921,510,907,788,019,393,178,114,194,545,257,223,865,541,461,062,892,187,96 0,223,838,971,476,088,506,276,862,967,146,674,697,562,911,234,082,439,208,160,153,780,889,893,964,518,263,243,671,616,762,179,168,909,779,911,903, 754,031,274,622,289,988,005,195,444,414,282,012,187,361,745,992,642,956,581,746,628,302,955,570,299,024,324,153,181,617,210,465,832,036,786,906,11 7,260,158,783,520,751,516,284,225,540,265,170,483,304,226,143,974,286,933,061,690,897,968,482,590,125,458,327,168,226,458,066,526,769,958,652,682, 272,807,075,781,391,858,178,889,652,208,164,348,344,825,993,266,043,367,660,176,999,612,831,860,788,386,150,279,465,955,131,156,552,036,093,988,18 0,612,138,558,600,301,435,694,527,224,206,344,631,797,460,594,682,573,103,790,084,024,432,438,465,657,245,014,402,821,885,252,470,935,190,620,929, 023,136,493,273,497,565,513,958,720,559,654,228,749,774,011,413,346,962,715,422,845,862,377,387,538,230,483,865,688,976,461,927,383,814,900,140,76 7,310,446,640,259,899,490,222,221,765,904,339,901,886,018,566,526,485,061,799,702,356,193,897,017,860,040,811,889,729,918,311,021,171,229,845,901, 641,921,068,884,387,121,855,646,124,960,798,722,908,519,296,819,372,388,642,614,839,657,382,291,123,125,024,186,649,353,143,970,137,428,531,926,64 9,875,337,218,940,694,281,434,118,520,158,014,123,344,828,015,051,399,694,290,153,483,077,644,569,099,073,152,433,278,288,269,864,602,789,864,321, 139,083,506,217,095,002,597,389,863,554,277,196,742,822,248,757,586,765,752,344,220,207,573,630,569,498,825,087,968,928,162,753,848,863,396,909,95 9,826,280,956,121,450,994,871,701,244,516,461,260,379,029,309,120,889,086,942,028,510,640,182,154,399,457,156,805,941,872,748,998,094,254,742,173, 582,401,063,677,404,595,741,785,160,829,230,135,358,081,840,096,996,372,524,230,560,855,903,700,624,271,243,416,909,004,153,690,105,933,983,835,77 7,939,410,970,027,753,472,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000,000,000 •Whack off 7 of the zeros and divide by three to get the number of years to use Mallows method in a small ML problem 03/19/2019 San Francisco Federal Reserve 2017 18
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0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 s20_gt50 - perfect classification of "high yield" also (which was defined as > 170 bpa). s20gt50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 33 42 48 52 56 61 66 71 72 77 76 82 86 88 91 93 96 98 101 103 106 108 110 112 114 117 118 121 123 120 125 126 128 129 130 131 132 134 135 136 137 138 140 141 142 143 144 146 147 148 149 150 151 152 153 154 155 156 157 158 160 160 161 163 164 167 168 169 170 173 173 175 177 179 183 184 184 191 193 202 205 215 230 271 s3_s20_gt50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 The pTrees for the 1691 pixel crop yield data (in value asc order). [Line_numbers, values, pTrees]
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Kilo, Mega, Giga, Tera, Peta Kilobyte (KB): 210 bytes = 1,024 bytes ~ 1,000 bytes Approximate size: one e-mail (plain text) Desktop Example: TRS-80 w/4 KB RAM (1977) Megabyte (MB): 220 bytes = 1,048,576 bytes ~ 1,000,000 bytes Approximate size: 30 phonebook pages Desktop Example: IBM PS/2 PC w/1 MB RAM (1987) Gigabyte (GB): 230 bytes = 1,073,741,824 bytes ~ 1,000,000,000 bytes Approximate size: 15 copies of the OKC white pages Desktop: c. 1997 Terabyte (TB): 240 bytes = 1,099,511,627,776 bytes ~ 1,000,000,000,000 bytes Approximate size: 5,500 copies of a phonebook listing everyone in the world Desktop: ??? (Jan 2009: 32 GB) Petabyte (PB): 250 bytes ~ 1,000,000,000,000,000 bytes Desktop: ??? Hardware Lesson CS1313 Spring 2009 44
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Bytes • How many bits is 6GB? = 6 x 230 bytes = 6 x 1,073,741,824 bytes = 6,442,450,944 bytes x 8 bits per byte = 51,539,607,552 bits Name byte kilobyte (KB) megabyte (MB) gigabyte (GB) terabyte (TB) Number of Bytes 1 1024 1,048,576 1,073,741,824 1,099,511,627,776 power of 2 20 210 220 230 240
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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0
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Storage Definitions and Notation Review The basic unit of computer storage is the bit. A bit can contain one of two values, 0 and 1. All other storage in a computer is based on collections of bits. Given enough bits, it is amazing how many things a computer can represent: numbers, letters, images, movies, sounds, documents, and programs, to name a few. A byte is 8 bits, and on most computers it is the smallest convenient chunk of storage. For example, most computers don’t have an instruction to move a bit but do have one to move a byte. A less common term is word, which is a given computer architecture’s native unit of data. A word is made up of one or more bytes. For example, a computer that has 64-bit registers and 64-bit memory addressing typically has 64-bit (8-byte) words. A computer executes many operations in its native word size rather than a byte at a time. Computer storage, along with most computer throughput, is generally measured and manipulated in bytes and collections of bytes. A kilobyte, or KB, is 1,024 bytes a megabyte, or MB, is 1,0242 bytes a gigabyte, or GB, is 1,0243 bytes a terabyte, or TB, is 1,0244 bytes a petabyte, or PB, is 1,0245 bytes Computer manufacturers often round off these numbers and say that a megabyte is 1 million bytes and a gigabyte is 1 billion bytes. Networking measurements are an exception to this general rule; they are given in bits (because networks move data a bit at a time). Operating System Concepts – 9th Edition 1.17 Silberschatz, Galvin and Gagne ©2013
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ADDRESS MAPPING (MULTIPLE CHANNELS) C Row (14 bits) Bank (3 bits) Column (11 bits) Byte in bus (3 bits) Row (14 bits) C Bank (3 bits) Column (11 bits) Byte in bus (3 bits) Row (14 bits) Bank (3 bits) Column (11 bits) Byte in bus (3 bits) Row (14 bits) Bank (3 bits) C Column (11 bits) C Byte in bus (3 bits) • Where are consecutive cache blocks? C Row (14 bits) High Column Bank (3 bits) C High Column Bank (3 bits) High Column C Bank (3 bits) High Column Bank (3 bits) High Column 8 bits Low Col. Byte in bus (3 bits) C Low Col. Byte in bus (3 bits) 3 bits 8 bits Row (14 bits) Byte in bus (3 bits) 3 bits 8 bits Row (14 bits) Low Col. 3 bits 8 bits Row (14 bits) Byte in bus (3 bits) 3 bits 8 bits Row (14 bits) Low Col. Bank (3 bits) Low Col. C Byte in bus (3 bits) 3 bits 47
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Compressing the original digital image        0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.25 0. 0.5 0. 0. 0. 0.125 0.25 0.  0.5 0. 0. 0. 0.125  0.25 0. 0. 0.5 0. 0. 0.125  0.25 0. 0.  0.5 0. 0.  0.125 0. 0.25 0. 0. 0.5 0.  0.125 0. 0.25 0. 0.  0.5 0.  0.125 0.  0.25 0. 0. 0. 0.5  0.125 0.  0.25 0. 0. 0.  0.5 Transpose of Transforming Matrix W                               Original Matrix – this one describes the image 82 80 73 71 75 78 72 99 10 10 9 12 15 9 17 73 25 26 33 41 38 12 10 66 112 103 104 102 86 30 10 56 114 109 108 128 95 33 13 57 107 112 111 117 85 17 18 65 114 111 90 69 40 11 35 78 69 61 38 20 14 23 58 88 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125  0.125  0.125  0.125  0.125 0.25 0.25  0.25  0.25 0. 0. 0. 0. 0. 0. 0. 0. 0.25 0.25  0.25  0.25 0.5  0.5 0. 0. 0. 0. 0. 0. 0. 0. 0.5  0.5 0. 0. 0. 0. 0. 0. 0. 0. 0.5  0.5 0. 0. 0. 0. 0. 0. 0. 0. 0.5  0.5 Transforming Matrix W        
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Measuring Memory Capacity • Kilobyte: 210 bytes = 1024 bytes – Example: 3 KB = 3 times 1024 bytes • Megabyte: 220 bytes = 1,048,576 bytes – Example: 3 MB = 3 times 1,048,576 bytes • Gigabyte: 230 bytes = 1,073,741,824 bytes – Example: 3 GB = 3 times 1,073,741,824 bytes
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Executing Machines Size Ones Hops Otters Otter Steps 6x2 (18268 digits) (36535 digits) 30345 > 99% 6x2 (10567 digits) (21133 digits) 99697 > 99% 6x2 (1440 digits) (2880 digits) 8167 > 99% 6x2 (882 digits) (1763 digits) 2211 > 99% 4x3 (7037 digits) (14073 digits) 25255 > 99% 4x3 (6035 digits) (12069 digits) 34262 > 99% 4x3 (4932 digits) (9864 digits) 57368 > 99% 3x4 (6519 digits) (13037 digits) 13667 > 99% 3x4 (2373 digits) (4745 digits) 13465 > 99% 3x4 (2356 digits) (4711 digits) 107045 > 99% 2x6 (4934 digits) (9867 digits) 16394 > 99% 2x6 (4932 digits) (9864 digits) 49142 > 99% 2x6 (822 digits) (1644 digits) Beaver, Platypus, Unicorn … 2733 Monash > 99% June 2nd, 2014
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Executing Machines Size Ones Hops Otters Otter Steps 6x2 (18268 digits) (36535 digits) 30345 > 99% 6x2 (10567 digits) (21133 digits) 99697 > 99% 6x2 (1440 digits) (2880 digits) 8167 > 99% 6x2 (882 digits) (1763 digits) 2211 > 99% 4x3 (7037 digits) (14073 digits) 25255 > 99% 4x3 (6035 digits) (12069 digits) 34262 > 99% 4x3 (4932 digits) (9864 digits) 57368 > 99% 3x4 (6519 digits) (13037 digits) 13667 > 99% 3x4 (2373 digits) (4745 digits) 13465 > 99% 3x4 (2356 digits) (4711 digits) 107045 > 99% 2x6 (4934 digits) (9867 digits) 16394 > 99% 2x6 (4932 digits) (9864 digits) 49142 > 99% HERE BE 2x6 (822 digits) (1644 digits) Beaver, Platypus, Unicorn … 2733 Monash > 99% June 2nd, 2014
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Executing Machines Size Ones Hops Otters Otter Steps 6x2 (18268 digits) (36535 digits) 30345 > 99% 6x2 (10567 digits) (21133 digits) 99697 > 99% 6x2 (1440 digits) (2880 digits) 8167 > 99% 6x2 (882 digits) (1763 digits) 2211 > 99% 4x3 (7037 digits) (14073 digits) 25255 > 99% 4x3 (6035 digits) (12069 digits) 34262 > 99% 4x3 (4932 digits) (9864 digits) 57368 > 99% 3x4 (6519 digits) (13037 digits) 13667 > 99% 3x4 (2373 digits) (4745 digits) 13465 > 99% 3x4 (2356 digits) (4711 digits) 107045 > 99% 2x6 (4934 digits) (9867 digits) 16394 > 99% 2x6 (4932 digits) (9864 digits) 49142 > 99% HERE BE HOBBITS! 2x6 (822 digits) (1644 digits) Beaver, Platypus, Unicorn … 2733 Monash > 99% June 2nd, 2014
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Terminology & Units of Measure • Basic unit of data storage in computer is the byte • Memory size (both primary and secondary) usually given in multiples of bytes: – – – – 1 K = 1 kilobyte = 1024 bytes 1 M = 1 megabyte = 1,048,576 bytes 1 G = 1 gigabyte = 1,073,741,824 bytes 1 T = 1 terabyte = 1,099,511,627,776 bytes 6
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Bytes • 1 bit (1/0) usually not useful on its own • Usually work in larger chunks – Byte : 8 bits – Special names for large collections of bytes: Name byte kilobyte (KB) megabyte (MB) gigabyte (GB) terabyte (TB) Number of Bytes 1 1024 1,048,576 1,073,741,824 1,099,511,627,776 power of 2 20 210 220 230 240
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Bytes • How many bits is 6GB? Name byte kilobyte (KB) megabyte (MB) gigabyte (GB) terabyte (TB) Number of Bytes 1 1024 1,048,576 1,073,741,824 1,099,511,627,776 power of 2 20 210 220 230 240
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Orders of Magnitude  One 0/1 (“no/yes”) “bit” is the basic unit of memory  Eight (23) bits = one byte  1,024 (210) bytes = one kilobyte (1K)*  1,024K = 1,048,576 (220 bytes) = one megabyte (1M)  1,024K (230 bytes) = one gigabyte (1G)  1,024 (240 bytes) = one terabyte (1T)  1,024 (250 bytes) = one petabyte (1P)  ... 280 bytes = one yottabyte (1Y?) 17 CMSC 100 -- Just Bits Tue 9/11/12
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Measuring Memory  One 0/1 (“no/yes”) “bit” is the basic unit of memory        Eight (23) bits = one byte 1,024 (210) bytes = one kilobyte (1K)* 1,024K (220 bytes) = one megabyte (1M) 1,024K (230 bytes) = one gigabyte (1G) 1,024 (240 bytes) = one terabyte (1T) 1,024 (250 bytes) = one petabyte (1P) ... 280 bytes = one yottabyte (1Y?)  How many different patterns can you represent with one bit of storage?  Two! (It’s either 0 or 1; that’s it, no in between)  How many different patterns can you represent with one byte of storage? Note that external storage is usually measured in decimal rather than binary Thu 9/1/2011 CMSC 100 -- Overview (1000 bytes = 1K, and s 14
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Measuring Memory  One 0/1 (“no/yes”) “bit” is the basic unit of memory         How many different patterns can you represent with one bit of storage?   11 * Eight (23) bits = one byte 1,024 (210) bytes = one kilobyte (1K)* 1,024K (220 bytes) = one megabyte (1M) 1,024K (230 bytes) = one gigabyte (1G) 1,024 (240 bytes) = one terabyte (1T) 1,024 (250 bytes) = one petabyte (1P) ... 280 bytes = one yottabyte (1Y?) Two! (It’s either 0 or 1; that’s it, no in between) How many different patterns can you represent with one byte of storage? Note that external storage is usually measured in decimal rather than binary (1000 bytes = 1K, and so on) CMSC 100 -- Overview Thurs 8/30/12
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366 366 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 201 201 650 650 354 354 846 846 668 668 583 583 480 480 916 916 858 858 797 797 339 339 887 887 768 768 610 610 443 443 211 211 273 273 491 491 317 317 332 332 990 990 556 556 295 295 203 203 207 207 502 502 625 625 656 656 681 681 685 685 332 332 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 730 730 560 560 481 481 245 245 686 686 826 826 842 842 615 615 441 441 900 900 781 781 964 964 940 940 631 631 313 313 569 569 388 388 889 889 367 367 823 823 874 874 997 997 999 999 689 689 513 513 412 412 437 437 872 872 218 218 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 500 500 274 274 741 741 244 244 207 207 935 935 420 420 418 418 670 670 752 752 870 870 781 781 587 587 364 364 794 794 574 574 566 566 959 959 795 795 286 286 679 679 508 508 788 788 687 687 657 657 489 489 321 321 380 380 540 540 842 842 613 613 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 991 991 801 801 476 476 335 335 725 725 593 593 250 250 759 759 603 603 317 317 959 959 313 313 924 924 754 754 442 442 541 541 256 256 973 973 746 746 322 322 901 901 857 857 665 665 353 353 342 342 853 853 580 580 324 324 603 603 785 785 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 524 524 423 423 654 654 745 745 804 804 777 777 580 580 298 298 494 494 867 867 228 228 613 613 730 730 540 540 283 283 959 959 937 937 639 639 476 476 577 577 499 499 877 877 453 453 564 564 417 417 986 986 438 438 791 791 653 653 356 356 809 809 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 871 871 518 518 600 600 912 912 221 221 995 995 658 658 240 240 625 625 355 355 874 874 701 701 726 726 358 358 873 873 298 298 287 287 794 794 451 451 952 952 428 428 469 469 312 312 786 786 867 867 766 766 680 680 797 797 402 402 315 315 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 201 201 248 248 844 844 882 882 368 368 292 292 642 642 211 211 291 291 563 563 801 801 748 748 634 634 259 259 549 549 361 361 756 756 432 432 549 549 385 385 662 662 626 626 702 702 328 328 603 603 970 970 756 756 939 939 351 351 468 468 342 342 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 996 996 565 565 998 998 278 278 700 700 275 275 550 550 945 945 238 238 915 915 432 432 381 381 815 815 528 528 361 361 702 702 683 683 561 561 573 573 678 678 707 707 883 883 863 863 699 699 776 776 652 652 500 500 347 347 790 790 644 644 924 924 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 394 394 351 351 683 683 758 758 667 667 481 481 595 595 264 264 792 792 689 689 696 696 752 752 843 843 319 319 660 660 894 894 929 929 691 691 782 782 234 234 734 734 981 981 452 452 655 655 444 444 339 339 286 286 895 895 880 880 795 795 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 MONTH-BY-MONTH TABULATION OF VEHICLES ENTERING PARKING GARAGE ------------------------------------------------------------1: +++++########$$$$$$$$$$$ 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 (Min.: 201 Max.: 990 (Min.: 218 Max.: 999 (Min.: 207 Max.: 959 (Min.: 250 Max.: 991 5: +++++##########$$$$$$$$$ (Min.: 228 Max.: 986 Mean: 612) 6: +++++##########$$$$$$$$$ (Min.: 221 Max.: 995 Mean: 604) 7: +++++########$$$$$$$$$$$ (Min.: 201 Max.: 970 Mean: 540) 8: +++++###########$$$$$$$$ (Min.: 238 Max.: 998 Mean: 643) 9: +++++##########$$$$$$$$$ (Min.: 234 Max.: 981 Mean: 631) 10: ++++++#########$$$$$$$$$ (Min.: 252 Max.: 967 Mean: 601) 11: +++++#########$$$$$$$$$ (Min.: 204 Max.: 935 Mean: 592) 12: +++++#########$$$$$$$$$$ (Min.: 211 Max.: 964 Mean: 566) 2: +++++###########$$$$$$$$$ 3: +++++#########$$$$$$$$$ 4: ++++++#########$$$$$$$$$ CHAPTER 4 - RepetitionStructures Mean: 540) Mean: 655) Mean: 588) Mean: 611) 323 323 461 461 263 263 261 261 712 712 856 856 636 636 558 558 527 527 438 438 572 572 600 600 322 322 458 458 790 790 451 451 861 861 967 967 898 898 780 780 440 440 955 955 301 301 252 252 827 827 619 619 687 687 964 964 257 257 900 900 723 723 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 457 457 283 283 604 604 381 381 432 432 935 935 640 640 730 730 291 291 594 594 503 503 597 597 834 834 607 607 505 505 750 750 625 625 685 685 516 516 204 204 766 766 280 280 698 698 890 890 593 593 797 797 597 597 504 504 828 828 642 642 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 485 485 964 964 704 704 341 341 499 499 305 305 794 794 961 961 689 689 222 222 463 463 244 244 711 711 305 305 877 877 891 891 677 677 777 777 883 883 211 211 301 301 766 766 693 693 374 374 252 252 335 335 699 699 472 472 455 455 494 494 728 728 47
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