[Recover Note] For Computer Organization Quiz 1

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COMP1003 Computer Organization – Lecture 1: What is a Computer

1. Definition of Computation and Algorithm

• Computation: Any arithmetic or non-arithmetic calculation that follows a well-defined model, such as an algorithm.
• Algorithm Example: Euclid’s Algorithm for computing the greatest common divisor (GCD).

2. Human Computers

• Before modern computers, “computer” referred to a person performing mathematical calculations.

3. Comparison of Different Computing Devices

• Abacus vs. Modern Computer: Differences lie in speed, accuracy, and automation.
• Mechanical Computers vs. Modern Computers: Mechanical devices are limited in functionality compared to modern digital machines.
• Calculators vs. Modern Computers: Calculators perform specific mathematical tasks, while computers are general-purpose machines.
• Human Computers vs. Modern Computers: Machines replaced human labor for efficiency and complexity in computation.

4. Definition: Modern Computer

• A digital electronic general-purpose machine that automatically follows instructions (program) to solve problems.

5. Hardware vs. Human Brain Analogy

• Brain (CPU), Paper (Storage), Eyes (Input), and Hands & Pen (Output).

6. The Turing Machine

• Developed by Alan Turing in 1936, it is an abstract model of computation.
• Consists of a tape, read/write head, state register, and instruction table.
• The Church-Turing Thesis states that everything computable can be computed by a Turing machine.

7. Generations of Computers

• Generation Zero: Mechanical calculating machines (1642-1945).
• Generation One: Vacuum tube computers (1945-1953).
• Generation Two: Transistor computers (1954-1965).
• Generation Three and Four: Integrated Circuits (IC) and Very-Large-Scale Integration (VLSI) computers (1965-1980+).

8. The von Neumann Architecture

• Stored-program architecture: Both data and programs are stored in memory.
• Consists of CPU, ALU, registers, memory, I/O system.
• Von Neumann bottleneck: CPU faster than memory, forcing the CPU to wait for data.

9. Abstraction in Computing

• Abstraction: Simplifying a concept by focusing on important aspects and ignoring irrelevant details.
• It allows us to manage complexity by dividing systems into levels (hardware, software, etc.).

10. Levels of Abstraction in Computing

• User Level: Applications such as executable programs.
• High-Level Language: Programming languages like C, Java.
• Assembly Language: Low-level programming.
• Machine Language: Instruction set architecture.
• Control Level: Micro-code or hardwired.
• Digital Logic: Circuits and gates.

11. Hardware vs Software

• Hardware is faster but fixed, whereas software is more flexible but slower.

12. Transformation Levels

• Problems are broken down into algorithms and then implemented into programs. These programs are further transformed into machine instructions and circuit operations.

Lecture 2: Bits: Data Representation and Manipulation

1. Introduction

• Computers are essentially number-crunching machines that input, manipulate, and output numbers.
• Various number systems have been developed over time, such as Egyptian, Roman, Chinese, and Hindu-Arabic systems.

2. Binary System

• The binary system (base 2) is the foundation of computer operation, consisting of only two digits: 0 and 1.
• Leibniz’s Dream: Leibniz envisioned a machine using binary numbers for logical calculations, allowing problems to be solved like mathematical equations.

3. Bits and Bytes

• A bit (Binary Digit) is the smallest unit of data in a computer, representing either 0 or 1.
• Byte: A group of 8 bits. Computers handle data in chunks like bytes, words, etc.

4. Numeric Data Representation

• Unsigned Integers: Represent non-negative integers using binary digits.
• Signed Integers: Represent both positive and negative integers using a sign bit.
  • Sign-magnitude, 1’s complement, and 2’s complement methods are used to represent signed integers.
  • Two’s complement is the most commonly used method for representing negative numbers.

5. Base Systems

• Base 10 (Decimal): Human-readable numbering system.
• Base 2 (Binary): Used by computers.
• Base 16 (Hexadecimal): Common in computing for representing binary numbers more compactly.

6. Two’s Complement Representation

• A method for representing negative numbers by inverting all bits (1’s complement) and adding 1.

7. Real Numbers Representation

• Floating-point numbers: Real numbers are represented with a floating decimal point, enabling the representation of very large or small numbers.
• Example: IEEE 754 Standard for representing floating-point numbers (single and double precision).

8. Non-numeric Data Representation

• Computers also represent non-numeric data like text, audio, images, and video:
  • ASCII Code: Represents text using binary values.
  • Unicode: A larger character set supporting international characters.
  • Digital Audio: Represented by sampling analog signals into binary.
  • Images and Video: Represented as streams of pixels with color values in binary.

9. Operations on Bits

• Binary Arithmetic: Computers perform operations such as addition and subtraction using binary rules.
• Boolean Logic: Logical operations (AND, OR, NOT, XOR) are fundamental in computing.

10. Overflow and Sign Extension

• Overflow: Occurs when a calculated result exceeds the number of bits available.
• Sign Extension: Extending the number of bits of a signed integer by replicating the sign bit.

11. Boolean Logic Operations

• Developed by George Boole, these operations form the basis of decision-making in computers.
• Truth Tables: Used to evaluate the result of logical operations.

12. Exercises and Examples

• Practical examples are given on binary addition, subtraction, and conversion between base systems.
• Exercises focus on applying two’s complement representation, floating-point representation, and Boolean logic.

Lecture 3: Boolean Algebra – From Bits to Logic:

1. Introduction to Boolean Logic

• Computers use bits (0 and 1) to represent data, and Boolean logic is the system used to manipulate these bits.
• Boolean logic operations correspond to algebraic operations, making it a critical component in computer operations.

2. Boolean Algebra

• Algebra: The study of mathematical symbols and their manipulation. The term comes from the Arabic “al-jabr,” meaning “reunion of broken parts.”
• George Boole (1815-1864) created Boolean algebra, bridging logic and mathematics in his 1854 work, “An Investigation of the Laws of Thought.”

3. Boolean Variables and Operators

• Boolean Variables: Can only have two values (true/false, or 1/0).
• Boolean Operators:
  • AND (A ∧ B)
  • OR (A ∨ B)
  • NOT (¬A)
  These operations can be visualized using truth tables and Venn diagrams.

4. Boolean Functions

• A Boolean function takes at least one Boolean variable and operator to produce a Boolean result (0 or 1).
  • Example: F=X+YZ′F = X + YZ’F=X+YZ′
• Precedence: Operations follow the precedence of NOT > AND > OR.

5. Simplifying Boolean Functions

• Boolean functions are simplified to reduce the complexity of digital circuits, leading to cheaper, faster, and more power-efficient designs.
• Boolean Identities: These identities, such as (X+Y)′=X′Y′(X + Y)’ = X’Y'(X+Y)′=X′Y′, help simplify expressions.

6. DeMorgan’s Law

• DeMorgan’s law is useful for finding the complement of Boolean functions:
  • (A⋅B)′=A′+B′(A \cdot B)’ = A’ + B'(A⋅B)′=A′+B′
  • (A+B)′=A′⋅B′(A + B)’ = A’ \cdot B'(A+B)′=A′⋅B′

7. Canonical Forms

• Sum-of-Products (SOP): Logical expressions where different “product” terms are “summed.”
  • Example: F=AB+A′CF = AB + A’CF=AB+A′C
• Product-of-Sums (POS): Logical expressions where different “sum” terms are “multiplied.”
  • Example: F=(A+B)(A′+C)F = (A + B)(A’ + C)F=(A+B)(A′+C)

8. Binary Addition in Boolean Algebra

• Binary arithmetic operations differ from Boolean operations. Binary addition can be expressed using Boolean algebra and simplified for digital circuits.

9. Karnaugh Map (K-Map)

• A Karnaugh map is a visual method to simplify Boolean expressions, reducing the need for extensive Boolean identities.

10. Truth Table for Boolean Functions

• Truth tables represent all possible inputs and their corresponding outputs for Boolean expressions. They are essential for verifying the accuracy of simplifications.

11. Importance of Simplification

• Simplified Boolean expressions lead to more efficient hardware design, as simpler circuits require fewer components and resources.