COMP8830 System Architecture Lecture 2 Notes

Instructions, Numbers & Logic - Part I

Introduction

• This lecture provides an outline understanding of the operation of CPUs and memory in a stored-program (Von Neumann) computer.
• Covers fetch-execute cycle, simple instructions, memory addressing, and CPU registers.
• Explains how to read, write, and inter-convert numbers between bases 10, 16, 8, and 2, including conventional notations.

Key Milestones in AI and Computing

• AlphaGo: In a milestone for artificial intelligence, AlphaGo beat a human Go champion.
• Deep Blue: In 1996, Deep Blue was the first machine to win a chess game against a world champion.

Endgame Databases in Chess

• Endgame databases are generated in advance.
• All endgames with seven or fewer pieces are analyzed completely.
• Seven-piece database requires 200 TB.

The Basic Principles of Computers

• Stored-Program: The lecture references "The Basic Principles of Computers for Everyone" by J. Clark Scott, focusing on the concept of stored-program computers.
• Arithmetic: Chapter 1 and sections 3.1-3.2 of "Computer Organization and Design" by David A. Patterson and John L. Hennessy are suggested for background and arithmetic.

Types of Computers

• Stored-program: Computers that store programs in memory.
• Control-flow: Computers that execute instructions in a sequential manner.
• Digital: Computers that use discrete values to represent data.
• Electronic: Computers that use electronic components.
• Semiconductor-based: Computers that use semiconductors.

Von Neumann Architecture

• Programmable computers have a program (collection of instructions) and data (input and working data).
• In stored-program computers (Von Neumann architecture), both programs and data are stored in the same memory.
• This allows programs to help run/write other programs (self-application or bootstrapping).
• Programs (instructions) are just a kind of data.

Operating Systems

• The operating system is a program for running other programs.
• Before operating systems, human operators were required.

Computer Program Execution

• Programs consist of machine instructions and other data stored in memory.
• CPUs operate in an endless loop: fetch an instruction, execute it, fetch the next instruction.
• Instructions can jump to other parts of the program for repetitions.
• Instructions can be conditional, depending on computed results.

CPU Operation Example

• Instructions are fetched from memory, and operations are performed in functional units such as the ALU (Arithmetic Logic Unit).
• The program counter (PC) keeps track of the current instruction's address.
• Example assembly code (6502 CPU):
  • LDA $1025 ; load a number from memory location 1025
  • ADC $1026 ; add to it the number that's in location 1026
  • STA $1027 ; store the result to location 1027

Assembly vs Encoded Instructions

• Assembly language is a human-readable notation.
• When running, instructions are encoded as numbers.
• The processor reads these encoded instructions from memory.
• The PC (program counter) is a special register that points at the current instruction.

Memory Addresses

• Cells in memory are numbered sequentially, with each cell's number being its address.
• The program counter holds the address of the current instruction.

Representing Numbers

• Digital electronics encode numbers in a discrete and symbolic way.

Representing Numbers: Base Systems

• Tally Marks: xoxo |
• Roman Numerals: XII
• Decimal (Base Ten): 12

Decimal Numbers

• The decimal numeral 943 represents:
  • 9 hundreds + 4 tens + 3 units
  • 9 \times 10^2 + 4 \times 10^1 + 3 \times 10^0
• A digit's significance depends on its position.
• Significance uses powers of 10.

Powers

• x^n means multiply together n copies of x.
  • e.g., ten to the power 2 is a hundred
  • ten to the power 3 is a thousand
• 10^0 = 1 (not 0)
• 1 is the "do nothing" of multiplication.

Powers and Bases

• In base 8, "100" means sixty-four:
  • 1 sixty-four + 0 eights + 0 units
  • 1 \times b^2 + 0 \times b^1 + 0 \times b^0

Binary Numbers

• What number does the binary numeral 101010 represent?
  • 32s + 16s + 8s + 4s + 2s + 1s
  • 1\times32 + 0\times16 + 1\times8 + 0\times4 + 1\times2 + 0\times1 = 32 + 8 + 2 = 42

Hexadecimal (Base 16)

• Programmers often use base 16 (hexadecimal).
• Use letters A, B, C, D, E, F for digits ten to fifteen.
• Twelve is C, Forty-two is 2A, etc.

Why Hexadecimal?

• Low-level programming sometimes involves individual wires or binary digits.
  • Example: