Data Representation: Binary, Denary, and BCD

Information Representation

Data Representation

• Any number system relies on a base, indicating the count of digits, and place value, which specifies the value of each digit's position.
• Denary uses a base of 10, whereas binary uses a base of 2.
• Binary systems have bits (0s and 1s).
• All data and characters are represented in binary form.
• For example, 65 in binary is 0100001.

Denary vs. Binary Prefixes

• Denary prefixes: They include kilo- (k) with a factor value of ×10^3, mega- (M) with ×10^6, giga- (G) with ×10^9, and tera- (T) with ×10^12.
• Binary prefixes: They include kibi- (Ki) with a factor value of ×2^10, mebi- (Mi) with ×2^20, gibi- (Gi) with ×2^30, and tebi- (Ti) with ×2^40.

Binary Coded Decimal (BCD)

• This system represents each positive denary digit using a 4-bit sequence (nibble).
• Only certain digits undergo conversion to BCD, as particular digits may denote a value exceeding 9.
• In BCD, 429 translates to: 4 = 0100 | 2 = 0010 | 9 = 1001
• Concatenating the nibbles gives: 0100 0010 1001

Applications

• Practical uses: Strings of digits on electronic displays (e.g., calculators), precise measurement of decimal fractions and electronic coding of denary numbers.

Two's Complement

• Represents negative binary numbers with the Most Significant Bit (MSB) indicating the sign.
• Converting a negative denary number into binary such as -42: First, 42 = 101010. Then, add extra 0s: 00101010. Now, find one's complement of binary number by flipping the bits 11010101.
• Convert binary number to two's complement by adding 1, leading to |1010101+1= 11010110.
• To convert the binary two's complement into denary: Flip all the bits | 00101001 then add 1 | 00101010. Now convert binary to denary and add a -ve sign) | -42
• In 8 bits, the maximum positive number is 256, while the maximum negative number is -128.

Hexadecimal Systems

• Use a base of 16 with digits 0 to 9 and A to F (A to F equal 10 to 15).

Apllications

• Practical uses: Defining colours in HTML, defining Media Access Control (MAC) addresses, assembly languages, machine code, and debugging via memory dumps.
• A5 in denary translates as: (16×10) + (1×5) = 165
• 65 in hexadecimal translates as: 65+16=4 Remainder 1. = 41

Character Sets

• A character set encompasses upper and lower case letters, number digits, and punctuation marks.
• Via character encoding, character sets utilize different binary representations for each one.
• Character Encoding Standards: ASCII, Extended ASCII, and Unicode

ASCII

• English alphabets can be represented.
• Each character encoding occupies 7 bits and hence 128 possible characters.
• It requires smaller storage space.

Extended ASCII

• It is an extension of ASCII
• Most European languages' alphabets are included
• Extended to 8 bits, leading to 256 possible characters.

Unicode

• It is a superset for both ASCII and extended ASCII, and recognizes various global languages.
• It provides a greater range of characters via 2 or 4 bytes per character which requires 2 or 4 times more storage space for each character.

Multimedia

Bitmap Images

• The data for bitmapped images is encoded by assigning a solid colour to each pixel via bit patterns.
• Bit patterns are generated by considering each row of the grid as a series of binary colour codes matching each pixel's colour.
• Pixels are mapped onto main memory.
• Meta data containing the image size and number of colours reside in the File Header of the bitmap file.

Image Resolution

• When image resolution increases, the image becomes sharper or more detailed, and it is measured by the count of pixels/cm.
• Screen Resolution: It indicates the number of pixels viewable horizontally and vertically on the device's screen computed through: Number of pixels = width x height such as 1680 x 1080 pixels.

Colour depth

• It specifies the number of bits for representing a single pixel's colour.
• For n bits, the image has 2^n colours per pixel.
• For instance, a 16-colour bitmap possesses 4 bits per pixel and 2^4 = 16.
• Increasing colour depth improves colour quality, but also the file size.
• It is computed as follows: File Size = Number of Pixels × colour depth
• To convert bits to bytes, divide by 8.

Applications

• Scanned images and general computer usage benefit from small file size, which enables easy manipulation.

Vector Graphics

• Uses mathematical formulas to define drawing objects (shapes such as rectangles, lines, circles) for graphics creation.
• A drawing list refers to a set of commands which define the vector.
• The basic geometric data that dictate the shape and appearance are the properties of each object
• Object properties are recalculated if resized.
• They are scalable without loss of quality, unlike bitmaps.
• Applications: Commonly used for company logos.

Sound

• Continuous electrical signals form analogue data, while discrete electrical signals form digital data.
• Sound signals, naturally analogue, are vibrations via a medium and may contain infinite detail.
• Analogue signals undergo conversion (encoding) into digital signals via sampling.
• Sound wave's amplitude (height) gets sampled at set time intervals
• These samples are then encoded as a binary number sequence, providing a digital representation.

Sampling Rate

• It specifies the number of samples recorded per unit of time.
• The accuracy of the digitized sound wave representation can be increased by increasing it, at the cost of increased file size.

Sampling Resolution

• It determines the number of bits employed for encoding each sample.
• Increasing accuracy of the digitized sound wave increases file size.
• Bit Rate specifies the count of bits needed for storing one second of sound | Bit Rate = Sampling Rate × Sampling Resolution.
• File size is calculated as follows: File Size = Bit Rate * Length of Sound

Compression

• It reduces file size without significant quality loss which facilitates quicker data search and faster file transfers with less bandwidth.

Lossless Compression

• This compression type allows perfect reconstruction of original data from the compressed file using certain replacement methods.
• Some of the most common uses are in bitmap (.bmp), vector graphic (.svg) and .png images, text file compression, database records
• Run-length Encoding (RLE): A lossless method for compressing text and bitmap files that condenses sequences with adjacent, identical elements (characters in text file and pixels in bitmap images). These repeating sequences are encoded by a run count and run value.

Example of RLE in bitmap Image

• First row of an image, we can represent in a sequence of pixels as "W B B WWBBW" | W: white and B: black
• After applying RLE, the new representation is "W 2B 2W 2B W" where “2B” states “run” is 2, “run value” is B

Lossy Compression.

• This compression form eliminates the data that is unnecessary, reduces file accuracy more quickly, but achieves a smaller file size. Common sound files (.mp3) or .jpeg images use it.
• Perceptual Coding, utilized by .mp3 files, discards less noticeable parts of sound.

Communication

Networks and the Internet

• Networking devices facilitate fast data transmission by interlinking different devices within the network.
• Networking offers benefits such as file sharing between devices, shared access to output devices/software, and greater storage through network-connected mediums.
• LAN (Local Area Network) connects devices within a small area privately for transmission via cables or Wi-Fi.
• WAN (Wide Area Network) connects devices across larger areas, either for private or public use through PSTN connections or satellite links.
• Client-server Model: Server-based network relies on a dedicated server for providing applications to client computers, managing administration of resources and security.

Examples

• Printer manages print jobs from computers, File Sharing ensures access to stored files.
• Clients send server login requests for processing of valid user IDs and passwords.

Server Examples

• Proxy, Email, Database, and Domain controller

Thin Clients vs. Thick Clients

• Thin Clients depend mainly on the server's resources and provide output while Thick Clients can operate independently with more processing done on the device.

Peer-to-peer network model (P2P)

• It decentralizes, enabling computers to operate as both clients and servers, providing advantages in cost and traffic management over client-server models.

Client- server vs. Peer-to-peer models

• Client-server features include centralized backup and security. Central files in server prevent illegal resource usage, But require greater initial setup cost
• Client-server model can't work if server goes down Peer-to-peer are less traffic since data can be sent from different sources.

Network Topologies

• Bus, Star, Mesh and Hybrid
• Bus topology: Single lines which connect the devices, must have terminators at each end.
• One computer can read the data sent from one computer to another.

Star topology

• A central server ('Switch') handles communication with dedicated connections for each computer and does not cause collisions possible.

Mesh topology

• Every device is directly connected to the each other
• Mostly used for wireless networks connects via the routers,
• Hybrid: Combination of the different topologies like if there
• Other Wired Networks include Copper, Fiber-Optic Cables, and Wireless Networks used for data transmission

Wired Networks

• Ethernet, Bit Streaming

Copper Cable

• Less expensive and easier to install with flexible terminations though susceptible to electromagnetic charges.

Fiber-Optic Cables

• Improved security with broad bandwidth with reduced needs for boosting, suiting long distance communications, but requires expensive optical transmitters.

Wireless Networks.

• Connectivity is based on radio waves, microwaves, or satellites.

Radio Waves

• They are less expensive for TV signals while vulnerable to interference.

Micro-waves

• Uses larger bandwidth, can transfer more data at a time. But Emitting towers expensive to build, physical obstacles can interfere

Satellites

• Can be for Satellite phones and broadcast, they are inexpensive and easy to interfere

Ethernet

• Common for wired data transmission that prevents collisions using CSMA/CD methods,
• Bit Streaming is sequence of digital signals for fast data communication that relies on broadband speeds and buffers

Real-time vs On-demand bit streaming.

• Real-time streaming transfers live video signals but has higher broadband needs,
• On-demand streaming uses stored files and allows for pausing.

Cloud Computing

• cloud Computing: On-demand provision of data and operations through the Internet, offering scalable Infrastructure, platforms, and public/private cloud selections.
• Benefits include low technical knowledge needed, easy to implement and Flexibility.

Drawbacks

• Poor data privacy, and bandwidth problems, makes it cannot access the resources.

World Wide Web

• Collection of web pages stored on websites.
• Protocols are used to transmit data across the WWW

Internet

• The massive, open network of networks Use TCP/IP protocol Uses IP addresses Access provided by Internet Service Provider Communication used are wired, radio and satellite

Router

• Router is in each Network that connects two networks that operates in different protocols and connects internal and external connections for LANS / WANS, acts as a gateway & firewall.
• And are attached to the server. Router translate the to IP Addresses.

Switch

• It is Hardware device Connected to all LAN that broadcasts devices and Software function
• Switch, NIC, WNIC, WAP, Cable, Bridge, and Repeater are other devices connected to internet and communication for multiple LAN devices.
• Provides each device (an end-system) in the wired LAN with a unique
• Provides each device (an end-system) in the wired LAN with a unique

NetID and HostID

• NetID Identifies the network and HostID identifies devices. IP addresses are broken down to subnet .
• These subnet ID bits are used to identify each subnet and are public and private

Public IP Address

• Can be across the internet and and Private is only unique within LAN Range of IP addresses used for private IP addressing can never be assigned to public IP addresses

Static vs Dynamic IP Adresses.

• IP Static address never changes, dynamic never changes, depends if data privacy is less.

URL

• Uniform Resource Locator Provides unique reference addresses with protocols and location server.

Hardware

• Computers has a processor, output memory and,
• Most have systems and are part of small systems or general purpose.

Benifits

• They are mostly reliable and needs cheap mass production for users. Difficult to program functions some interfaces

Hardware Devices,

• Laser printer, 3D printer, speaker, magnet disk are all components as a hardware and output.

Laser Printer

• It draw image to create a light

3D Printer

• Object is then created and sealed from the light. And hardens by light.

Magnetic Hard Disk , Solid State (Flash) Memory, Optical Disk Reader/Writer components , are for reading and writing.

Sound

• Incoming sound moves the vibration and moves around creating the coil

Speaker

• Takes current creating a signal by the amplifier which makes noises.

Optical Disc Reader/Writer

• Reads disc with is shiny that is then read and send data

Touchscreen

• Touch the scream where it shows.
• There are capacitive and Resistive points which makes signals.

Monitoring and Control Systems

Monitoring System

• Some state external to computer system No changes made to environment by the system and hence no feedback

Control System

• Regulates the behaviour of other devices or systems. Event-driven system the controller alters the state of the system in response to some event. Time-driven system: the controller takes action at a specific point in time

Feedback Systems that affect

• Sensor Transfers cable output what affect input

Logic Gates And Logic Circuits.

• Logic Gates: use one or more inputs and produces a single logical output

• AND gate: If both inputs high, output is high (A・B)

• OR gate: If either inputs high, output is high (A+B)

• NOT gate: an inverter (A)

• NAND gate: (A・B) \n

• NOR gate: (A+B) \n

• XOR gate: (AB) \n

PROCESSOR FUNDAMENTAIS

• Data programs can exist to follow and the processors use registers,

Registers

• Registers store data that is on data or memory,
• The register store for decoding for instruction.

The Processor (CPU)

• Arithmetic and Logic Unit (ALU) operation to processor (ALU): part of processor that processes instructions which require some form of arithmetic or logical operation • Control Unit (CU): part of CPU that fetches instructions from memory, decodes them & synchronizes operations before sending signals to computer's memory, ALU and I/O devices to direct how to respond to instructions sent to processor • Immediate Access Store (IAS): memory unit that can be directly accessed by the processor • System Clock: timing device connected to processor that is needed to synchronize all components.

Buses

• It's a set of parallel wires that allow the transfer data between components in a computer system CPU, Memory Input (ALU, Registers, and Controls) and Output Data Bus Address Bus

Data bus

• Bidirectional bus that carries data .

Address bus

• Unidirectional bus that carries Address from processor to the CPU. .Control bus Ensure the conflict with using any device

Performance of Computer System Factors and clock speed

Bus Width

• Detrrmine the numbers simultaneously like in the numbers from the lines.

CHACHE MEMORY

• Commonly used instuction. Store more instruction, more faster it goes.

Ports.

HDMI

• is a high definition port to connect devices.

VGA

• only lets videos.

Fetch execute cycle

• MAR, PC, MDR, and other letters help with the cycles.
• IN what the data is in will the sqaure is whats in the register.

Interrupts

• Handles and service that lets things.
• By setting actions when enterrupted

Assembly language

• Process the machine with the code assembly , by transto one machine
• Symbolizing will help the processor code

D ata Movement Data Movement, Arithmetic ,compare .

Mode of AddreSING

• The address form. RELATIVE, conditional JUMP.
• It lets use jump easy
• lets divide easier
• bit to look at what it changed. And all it take

Operation Systems

• A set of program to help contr computers for different devices where the software can execute by commmunion

Memory management

• Use virtual Allocate Security and prevent

Files

Is the operating of the data

TRANNSLATORS.

• Some languages require different translattors and they all can be the same language

Intergereter

• Create and execute and use them and not be able to the run the program by testing the error
• Java some languahes 2 ways. Translati9n for

3Datavse and Dara moddelijng.

• File basedsystem data stored from a computee to alow user
• System is to database, that manages dssystems, and manipulates.
• The system is to model how can create and be the data.
• There all entities and objects

Relationel

• IS to model to to creae it and data to database s.
• Creates more databases and is is in use 2 and prevents from user. If it enters

Ethics and OWNERSHIP?

• Code has to be by ethic that guide conduct ethical and. Not only by copright.
• AL must be a machine copy and not hurt to
• Be careful of th threats by ware and
• Encryption is conversion but no illegal.