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computer science

CSCI 1001. overview of. computer science. REPRESENTING DATA II. bit: a value that is either 0 or 1. string: a sequence of bits. byte: a string of 8 bits. Bi nary. A bit string can represent a number:. 10110 =. 1×2 4 +0×2 3 +1×2 2 +1×2 1 +0×2 0. A byte has the place values: .

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computer science

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  1. CSCI 1001 overview of computer science REPRESENTING DATA II

  2. bit: a value that is either 0 or 1 string: a sequence of bits byte: a string of 8 bits

  3. Binary A bit string can represent a number: 10110 = 1×24+0×23+1×22+1×21+0×20 A byte has the place values: What is the smallest possible byte? the largest?

  4. 1 1 1 1011 0111 + 1 0 0 1 0 Binary Adding Rules 1 0 1 0 1 1 0 0 1 1 1 + + + + + 0 1 1 1 0 1 1

  5. 1000 = 000 111 001 110 010 101 011 100 Modular Arithmetic

  6. 1000 = 000 -1 = 8-1 001 -2 = 8-2 010 -3 = 8-3 011 -4 = 8-4 Two’s Complement

  7. 8-bit two’s complement: -x = 28-x 100000000 256-x = (255 –x) + 1 01101001 - 11111111 To compute -x: “flip” the bits & add 1! 01101001 - 100101 1 0 + 1 10010111 x-y = x + (256-y) = x-y + 256

  8. What do the following mean? 3.142 mantissa exponent 6.022 × 1023 1.616 × 10-35 base Mantissa Exponent Largest # 2 1 9.9×109 4 2 9.999×1099

  9. in binary: 0.1101₂ = 1×2-1+1×2-2+0×2-3+1×2-4 0.1101×211₂ = 1×22+1×21+0×20+1×2-1 Mantissa Exponent Largest # 4 4 0.1111×215 9 5 0.111111111×231 52 10 ≈21023 ≈ 10307

  10. http://cs1001.us/ Please read this article for Friday’s lecture: http://en.wikipedia.org/w/index.php?title=Markup_language&oldid=406618521

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