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Binary MathematicsCounting systemBase 10 counting systemNumbersBase 10 (Decimal numbers)Binary CodeBase 10 vs Base 2Binary Bits and BytesSlide 9Slide 10Base 10 to BinaryBinary mathematicsHexadecimal (base 16)Lookup tableExampleWisdom saidQuizAnswerBinary MathematicsCounting systemThere are three kinds of people in the world: those who can count, and those who can not. - Unknown WisdomToday’s classNumbering systemConversion between 10 based and 2 based numbering system.Binary Mathematics.QuizBase 10 counting systemWe happened to use the current counting system, because we happened to have ten fingers.If dinosaurs had ruled the earth, they would be happy to use a 8-based counting system.NumbersAncient AfricaNotches on a bone.Egyptians/RomanEach magnitude is represented by a symbol. Indian/Arabian (Modern numbering system)1,475,268Base 10 (Decimal numbers)What does 157 mean?157 = 1 x 100 + 5 x 10 + 7 x 1 = 1 x 102 + 5 x 101 + 7 x 100Binary CodeImagine a specie that only has two fingers. how can they count?  A computer is such kind of two-finger specie. 0 and 1Each place is the exponential of 2Base 10 vs Base 2Base 10157157 = 1 x 100 + 5 x 10 + 7 x 1 = 1 x 102 + 5 x 101 + 7 x 100Base 21011 = 1 x 23 + 0 x 22 + 1 x 21 + 1 x 201011 = 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1Binary Bits and Bytes1 bit is a single bit of information, a 1 or 0Only two possible values1 byte is 8 bits, an 8 bit word256 possible values from 0-255 base 10 or 00000000 to 11111111 base 210100110 is a single byteBase 10 to BinaryBinary mathematics0+0=01+0=11+1=10Hexadecimal (base 16) Binary code is too long in representation. Hex is much shorter.Converting a binary number to a Hex number is relatively easyEvery 4 bit can convert to a HexProblem: we are short of numbersA-10 B-11 C-12 D-13 E-14 F-15Lookup tableBinary Hex Binary Hex0000 0 1000 80001 1 1001 90010 2 1010 A0011 3 1011 B0100 4 1100 C0101 5 1101 D0110 6 1110 E0111 7 1111 FExampleWisdom saidThere are 10 kinds of people in the world, those who use binary counting system, and those who don’t.QuizNo Calculators!!!!Convert binary code to Decimal number.10100101 (Bin)Convert Decimal number to binary code176 (Dec)Convert Hexadecimal number to binaryBADDEFAdd these two binary numbers10001101+11011100=?Answer10100101 (Binary) = 165 (Decimal)176 (Decimal)= 10110000 (Binary)BADDEF=1011,1010,1101,1101,1110,1111The result of


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MSU LBS 126 - binary-03f

Course: Lbs 126-
Pages: 18
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