Computer Science Fundamentals Study Guide

Overview of Computer Science Foundations

  • Today's discussion involves key concepts in programming languages, focusing on how various programming languages translate into machine code and how computers represent numbers in binary, specifically negative numbers.

Special Occasion in Computer Science

  • Today is Ada Lovelace Day, celebrated on the second Tuesday of October.
    • Reward: Box of biscuits for answering correctly.

High-Level Languages, Machine Languages, and Machine Code

  • High-level Programming Languages: Examples include C, Python, etc. These are user-friendly and abstract the complexity of coding.
  • Machine Language: Refers to the set of instructions executed directly by a computer's CPU, using binary code.
  • Machine Code: The binary representation of machine language instructions that the computer can process.
    • This includes the assembler, which compiles high-level code into machine code, specifically for the 68000 processor.
Compiler Functionality
  • A compiler processes high-level programming code and converts it into assembly code, which is then transformed into machine code.
  • The machine code consists of binary instructions tailored for a specific architecture.
    • Example architecture discussed: 68000 processor.
Memory Representation
  • Memory is typically uniform; however, memory-mapped I/O confuses normal memory because it represents I/O devices with addresses, complicating direct interaction with memory.
  • Writing at a low level requires knowledge about device addresses and control mechanisms.

The Importance of the Program Counter

  • Program Counter (PC): Critical for the CPU to keep track of instruction execution.
    • Functionality: Points to executing instruction and fetches the next instruction following a fetch-decode-execute cycle.
  • The program counter needs to be initialized with the first instruction's address after compilation.
Differentiating Between Code and Data
  • While both appear as a series of bytes in memory, the CPU distinguishes between instructions (code) and data by referencing the program counter.
  • The operand field specifies the location of data necessary for instruction execution, allowing the CPU to navigate between code and data in memory.

Number Representation in Binary

  • Binary Numbers: Initially focused on representing positive integers; the discussion now progresses to negative integers.
  • **Sign-Magnitude Representation:
    • Positive numbers have the leftmost sign bit as 0.
    • Negative numbers utilize a leftmost sign bit as 1.
    • Example: 5 = 00000101, -5 = 10000101 (assuming 8-bit representation).
Issues with Sign-Magnitude Representation
  • Limitation: Introduces two representations for zero: a positive zero and a negative zero, complicating computation.
  • Cannot directly perform arithmetic operations like addition/subtraction using this approach.

Alternative Approaches

One’s Complement Representation
  • Convert positive binary numbers to negative by inverting the bits.
    • Example for -23:
    1. Positive: 00010111 (23)
    2. One’s complement: 11101000
    3. Adding positive and negative numbers requires carry-around logic; however, issues with zero representation persist.
Two’s Complement Representation
  • Transformation to Two’s Complement:
    1. Calculate One's Complement (invert the bits).
    2. Add 1 to the result.
  • Advantages of Two’s Complement:
    • Only one representation for zero.
    • Straightforward addition and subtraction, preserving correct results without ambiguity.
  • Example: Adding 56 (represented as 00111000 in binary) and -77 (calculated as two's complement):
    • 56 = 00111000
    • -77 = 10110001 (One’s complement of 77 is 01001110, add 1: 11001111)
Final Calculation:
  • If 56 + (-77) = 00111000 + 10110001 → binary calculation → binary adjustments lead to accurate results.
    • The negative result indicates that 56 - 77 = -21.
Summary of Numerical Range
  • In an 8-bit representation using two's complement, the range is from -128 to 127.
  • Attempting to add two numbers exceeding this range leads to overflow situations.

Transition to Boolean Algebra

  • Fundamental Concept in Computer Science: Boolean algebra is essential for understanding low-level operations and circuit design in computers.

  • Basic Logic Gates in Boolean Algebra:

    • AND Gate: Outputs true (1) if both inputs are true.

    • Truth Table:

      • 0 AND 0 = 0
      • 0 AND 1 = 0
      • 1 AND 1 = 1

    • OR Gate: Outputs true if at least one input is true.

    • Truth Table:

      • 0 OR 0 = 0
      • 0 OR 1 = 1
      • 1 OR 1 = 1

    • NOT Gate: Inverts the input value; outputs true for false and vice versa.

  • Representations of Logic Gates:

    • Logic gates represent conditional logic elements fundamental to computational processes.
Components of a Processor
  • Each logic gate can be constructed from transistors; complex processors are built from combinations of these gates designed to perform specific operations.

Conclusion

  • Understanding how high-level programming translates to machine operations assisted by knowledge of binary representation is critical in comprehending computer operation fundamentals.
  • Notions of logical operations and numerical representation, including negative numbers through techniques such as two's complement, are foundational for effective programming and electronic circuit design.