CS 231 Intro & Base ConversionsAnnouncementsTips for CS 231Slide 4Digits vs. bitsBinary to decimalDecimal to binarySlide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Hexadecimal baseSlide 17Binary to HexOctal baseSlide 20Binary to OctalOther conversionsSummaryCS 231Intro & Base ConversionsCelal ZiftciAug 26, 2005AnnouncementsMallard is up. Try to log on and take the first quiz (due Monday, Aug 29)Course webpage is downMallard link is posted on the newsgroup(https://mallard2.cites.uiuc.edu/CS231/)First homework assignment to be released sometime next weekTips for CS 231Don’t hesitate to:Ask questionsInterrupt when you don’t understandBe comfortable with binary and hexLearn device inputs & outputsAllows abstractionEasier to understandShow your workTips for CS 231Efficiency is important!Neatness is important!Unreadable solutions are considered wrongReadable ones are neat, short (big favor for both you and the graders)Digits = powers of 10… 100, 10, 1,1/10,1/100,1/1000 …… 102, 101, 100, 10-1, 10-2, 10-3 …Ex: (36.25)10 = 3*10 + 6*1 + 2*1/10 + 5* 1/100Bits = powers of 2… 8, 4, 2, 1,1/2,1/4,1/8 …… 23, 22, 21, 20, 2-1, 2-2, 2-3 …Ex: (100100.01)2 = 1*32 + 1*4 + 1*1/4Digits vs. bitsBinary to decimaladd powers that have a 1(101001)2 = 32 + 8 + 1(0.1001)2 = 1/2 + 1/16(10110.1011)2 = ?16 + 4 + 2 + 1/2 + 1/8 + 1/16= 22.6875Decimal to binaryLeft of decimal pointRepeatedly divide integer part by 2 until you get 0Read remainders bottom to up22 = (?)22211 R 05 R 12 R 11 R 00 R 1Decimal to binaryLeft of decimal pointRepeatedly divide integer part by 2 until you get 0Read remainders bottom to up22 = (10110)22211 R 05 R 12 R 11 R 00 R 1Decimal to binaryRight of decimal pointRepeatedly multiply fractional part by 2 until you get 1Read integer portion top to bottom0.8125 = (?)20.81251.62501.250.51.0Decimal to binaryRight of decimal pointRepeatedly multiply fractional part by 2 until you get 1Read integer portion top to bottom0.8125 = (0.1101)20.81251.62501.250.51.0Decimal to binaryWhat if there are both left and right of the decimal point?Do them separately and combine22.8125 = (?)2Decimal to binaryWhat if there are both left and right of the decimal point?Do them separately and combine22.8125 = (?)22211 R 05 R 12 R 11 R 00 R 10.81251.62501.250.51.0Decimal to binaryWhat if there are both left and right of the decimal point?Do them separately and combine22.8125 = (10110.1101)22211 R 05 R 12 R 11 R 00 R 10.81251.62501.250.51.0up downDecimal to binaryToy example 3.25 = (?)231 R 10 R 10. 250.501.0Decimal to binaryToy example 3.25 = (11.01)231 R 10 R 10. 250.501.0Hexadecimal baseHex digits = powers of 16… 256, 16, 1,1/16,1/256 …… 162, 161, 160, 16-1, 16-2 …use digits 0-9, A-FA=10, B=11, C=12, D=13, E=14, F=15often preceded by 0xbook subscript notation (24.4)16Ex: (24.4)16 = 2*16 + 4*1 + 4*1/16Hexadecimal baseHex (hexadecimal)Hex digit is a group of 4 bitsMemorize this table!!dec. hex binary0 0 00001 1 00012 2 00103 3 00114 4 01005 5 01016 6 01107 7 01118 8 10009 9 100110 A 101011 B 101112 C 110013 D 110114 E 111015 F 1111Hex (hexadecimal)Group from decimal point outwardPad with zeros to get groups of 4(1101101001010.101001)2(0001 1011 0100 1010 . 1010 0100)2 1 B 4 A . A 4(1101101001010.101001)2 = (1B4A.A4)16Binary to HexOctal digits = powers of 8… 64, 8, 1,1/8,1/64 …… 82, 81, 80, 8-1, 8-2 …use digits 0-7sometimes preceded by 0book subscript notation (24.4)8Ex: (44.2)8 = 4*8 + 4*1 + 2*1/8Octal baseOctalOctal digits are groups of 3 bitsPad with zerosdec. octal binary0 0 0001 1 0012 2 0103 3 0114 4 1005 5 1016 6 1107 7 111Octal baseOctalGroup from decimal point outwardPad with zeros to get groups of 3(1101101001010.101001)2(001 101 101 001 010 . 101 001)2 1 5 5 1 2 . 5 1(1101101001010.101001)2 = (15512.51) 8Binary to OctalWhat about other conversions such as:Octal HexDecimal Hex…Use other conversions you already knowOctal Binary HexDecimal Binary HexOther conversionsI. Decimal BinaryBinary DecimalII. Binary HexBinary OctalIII. Other conversionsUse the conversions you already
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