Computer Systems A - Data Representation and Computer Structure

Data Representation and Computer Structure

• All information inside computers is encoded as 0s and 1s (bits).

• Bits are the basic building blocks, combined to represent text, numbers, images, and sound.

• This is fundamental as computers manipulate digital signals (on/off, 1/0).

Key Ideas

• A bit is the smallest unit of data.

• $8 bits = 1 byte$

• Different data types are encoded into binary differently, requiring decoding based on type.

• Boolean logic calculates results as True or False.

• Buses connect components for data and signal transfer.

• System buses play a crucial role in the machine cycle, ferrying addresses, data, and control signals.

How Data Is Represented in a Computer System

• Data is represented as bit patterns using sequences of 0s and 1s.

• A bit is the smallest unit of data, either 0 or 1 (Off/False or On/True).

• 8 contiguous bits = 1 byte.

Integer Representation

Decimal to Binary Conversion

• Repeatedly divide the decimal number by 2, noting the remainders.

• Write the remainders in reverse order to get the binary representation.

Binary to Decimal Conversion

• Use the positional notation system, where each digit represents a power of 2, starting from the rightmost digit.

$10110<em>2 = (1×2^4) + (0×2^3) + (1×2^2) + (1×2^1) + (0×2^0) = 22</em>{10}$

$1101010<em>2 = (1×2^6) + (1×2^5) + (0×2^4) + (1×2^3) + (0×2^2) + (1×2^1) + (0×2^0) = 106</em>{10}$

Text Representation

• Text characters have binary representations using ASCII and Unicode.

• Standard ASCII uses a 7-bit code for 128 characters; Extended ASCII uses 8 bits.

• Unicode uses 16 bits per character to represent more characters.

Image Representation

• Images are represented using pixels, the smallest unit of a digital image.

• Each pixel is assigned a binary code to represent its color.

• A bitmap is an array/grid of binary data representing the color values of pixels.

Audio Representation

• Digital audio records sound as a sequence of samples.

• Each sample encodes the amplitude of the sound wave at a specific time.

• Examples of bit depths:

  • 8-bit audio: 256 values
  • 16-bit audio: 65,536 values
  • 24-bit audio: 16,777,216 values

Video Representation

• Digital videos are represented as a series of images (frames).

• Each frame is encoded using bit patterns to store the color of each pixel.

File Representation

• Files are represented as collections of bits following specific file formats.

• Examples: JPEG, DOC/DOCX, XLS/XLSX.

Data for Transmission

• Data is broken into packets for transmission over networks.

• Packets are reassembled at the destination.

Bit Patterns

• Allow efficient data processing, storage, and transmission.

• Foundation of modern computing systems.

Boolean Logic and Binary

• Boolean logic is a type of algebra with results as true or false.

• Used in digital devices like computers.

Logic Operations

• AND: Output is 1 (true) if both inputs are 1 (true).

• OR: Output is 1 (true) if either input is 1 (true).

• NOT: Output is the opposite of the input value.

Computer Memory: Units of Memory

• Measured in bytes.

  • Bit (b): Smallest unit, 0 or 1.
  • Byte (B): 8 bits.
  • Kilobyte (KB): 1024 bytes.
  • Megabyte (MB): 1024 KB or 1,048,576 bytes.
  • Gigabyte (GB): 1024 MB or 1,073,741,824 bytes.

Structure of a Computer System

• Comprises a processor/CPU, memory, input, output, and storage devices.

• CPU is the calculating, sorting, searching, and decision-making part.

• Main memory (RAM) stores data currently used by the CPU.

• Secondary storage stores saved computer data.

• Flip-flops are basic electronic circuits used for storing bits.

Types of Memory: RAM and ROM as Bit Storage

• RAM (Random Access Memory): Primary storage for data the CPU is actively using.

  • Volatile: Data is lost when power is off.

• ROM (Read-Only Memory): Non-volatile, retains data when power is off.

  • Used to store instructions for initializing hardware or loading the operating system.

• Secondary Memory/Storage: Non-volatile, external storage.

  • Examples: HDDs, SSDs, USBs, CDs.

• Cache Memory: Small, high-speed memory for temporary data storage on or close to the CPU.

• Registers: Fastest access, smallest capacity storage within the CPU.

Memory Hierarchy

• Hierarchical arrangement of memory types by speed, capacity, and cost.

• Registers (fastest, smallest) → Cache → RAM → Secondary Storage (slowest, largest).

Caching

• Hardware or software component that stores data for faster future requests.

• Browser cache: Temporary storage in RAM or on disk for recently downloaded web pages.

Central Processing Unit (CPU)

• Manages all data processing.

• Consists of the Control Unit (CU), Arithmetic and Logic Unit (ALU), and registers.

Components of a CPU

• Control Unit (CU):

  • Manages operations within the CPU.
  • Fetches and decodes instructions.
  • Manages data flow to ALU and registers.

• Arithmetic and Logic Unit (ALU):

  • Performs arithmetic and logical operations.

• Registers:

  • Fastest, smallest storage units within the CPU.
  • MAR: Stores memory address being read/written.
  • PC: Stores the address of the next instruction.
  • MDR: Holds data being transferred to/from the processor.

• Cache:

  • Temporarily stores data and instructions for faster access.

• Clock:

  • Sends out regular pulses to synchronize CPU components.
  • Clock speed measured in GHz.

• System Bus:

  • Connects processor to other components.
  • Address bus, data bus, and control bus.

Computer Buses – Outside of the CPU

• Connect the CPU to other components and main memory.

Machine Cycle

• Fetch, Decode, Execute, Store (FDES).

• CPU repeats this cycle to run programs.

Stages

1. Fetch: Retrieve instruction from memory.
2. Decode: Interpret the instruction.
3. Execute: Carry out the instruction.
4. Store: Store the results in memory or registers.

CPU Instruction Set

• Commands the CPU can understand and execute.

• Defines operations, data types, and addressing modes.

Embedded Systems

• Special-purpose computer system encapsulated by the device it controls.

• Pre-defined tasks, not programmable by users.

• Examples: fitness trackers, central heating systems.