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Foundations of computer science.org

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Introduction

Turing model

  • Data processors: Black box
  • Programmable data processors Program: A set of instructions telling the computer what to do.
  • Universal turing mechine Provide approriciate program with any commputer, the computer can do any computation.

Von Neumann model: Memory to store data and program

  • Four subsystem: memory, arithmetic logic unit, control unit, I/O Control unit: controls the operations of the memory, ALU I/O.
  • the stored program concept: Binary patterns in memory.
  • Program: Made of a squential finite number of instructions.

Computer components: Hardware, Data, Software.

  • Hardware: Four components under Von Neumann Model.
  • Data: Computer is a data processing mechine.
    • storing data: eletric signals’ presense and absence presentated by binary patterns
    • organizing data: units more than binary pattern.
  • Software:
    • Program storing: For reusablity.
    • Algorithms: How to consist instructions to be a approriciate program for sloving different problem.
    • Languages: Symbols and words to repersent binary.
    • Software Engineering: Structured programs.
    • operating systems: A serials of common used instructions works as manager to facilitate access to the computer’s componets by programs.

Computer science as DIscipline: Systems and applications

Data Representation and Operation

Number Systems

Positional Number Systems

\begin{multline} (SkSk-1…S2S1S0.S-1S-2…S-L)n=
Sk*nk+Sk-1*nk-1+…+S0*n0+S-1*n-1+…+S-L*n-L \end{multline} Position a Symbol occupies in the number determines the value.

  • Decimal System
  • Binary Digits(bits)
  • Hexadecimal System(base 16)
  • Octal System(base 8)
  • Conversion

Noposition Number Systems:Roman’s number

Data Storage

Data Types: Number, Text, Audio, Image, Video.

  • Engineering program: processes number with arithmetic logic operations.
  • Word Processing program: processes text as some kind of information.

Data inside computer

  • Bit Pattern: A squence of binary digits number. byte: eight digits binary number. Word: a longer bit pattern.

Storing number

  1. Integers
    1. Fixed-point representation
    2. Unsigned Representation no negative number, theoretical range could be between 0 to positive infinity, but actually there is a maximum unsigned integer.
      • Overflow: Drops the leftmost bit and keeps the rightside bits to fit the maximum bits.
      • Applications: Counter, Addressing, other types of data rather than number, which can be transformed into unsigned number.
    3. Sign&Magnitude Representation The available range for unsigned intergers is devide into two equal subranges, the first half ranges represents positive intergers, and the last range represents negative intergers. The leftmost bit is dedicate to store the sign which represents positive(+) or negative(-).
      • Overflow in Sign&Magnitude represent: the positive number will change the bit which represent positive or negative(if not large than two times as the subrange for positive intergers) the negative number will drops the leftmost bits, and may change the sign.
      • Applications: Part of real number, quantize an analog sign.
    4. Two’s complement representation