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Understanding Data Representation in Computer Science: Bits, Bytes, and Arithmetic

This resource provides an overview of fundamental concepts in computer science regarding data representation. It covers binary values, including bits (0s and 1s), byte representation (8 bits), and methods for binary addition and modular arithmetic. The concept of two's complement is explained for negative values, along with the significance of mantissa and exponent in scientific notation. Additionally, it addresses how various numbers can be represented in binary and the importance of these concepts in understanding computing technology.

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Understanding Data Representation in Computer Science: Bits, Bytes, and Arithmetic

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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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