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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)

**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.