Bits are the basic units of information in computing, representing values of 0 or 1. Bytes consist of 8 bits bundled together, allowing 256 possible values. Computer components like memory and storage are measured using multiples of bytes like kilobytes and megabytes. Binary numbers use bits like decimal numbers use digits, with each place value representing increasing powers of two rather than ten. Bytes are commonly used to represent text characters through encoding schemes like ASCII.
This document provides an overview of data representation in computer systems. It discusses how computers use binary numeric codes to represent different types of data like text, numbers, graphics and audio. These codes allow computers to interpret raw sequences of 0s and 1s as meaningful information. The document then explains binary number systems in more detail, how decimal numbers can be converted to and from binary, and how bytes and bits are used to store data in computer memory and represent characters. Specific examples are given of how binary representations are used in applications like robotics to control devices.
This lesson is for students taking the Cambridge School certificate exams Computer science subject(2210).I hope that it will of help to students in this period of crisis. Send me your feedback or suggestions on buxooa72@ gmail.com,
This document discusses binary numbers and how they are used in computers. It explains that computers use base 2 binary numbers represented by 0s and 1s rather than base 10 numbers. It provides examples of converting between base 10 and base 2 numbers. It also defines units of measurement for binary numbers, with the basic unit being a byte which is 8 bits. Larger units include kilobytes, megabytes, gigabytes and terabytes.
- The document discusses direct mapped caches including cache hit/miss terminology and how direct mapped caches work by mapping each memory word to a single cache block based on the memory address.
- It provides an example of a direct mapped cache with 1024KB capacity and 32-bit addresses, showing the cache block format and how an example address would map to a cache block and tag field.
- The document also discusses cache block size being larger than one word to improve cache performance and provides an example with a 4-word cache block.
The document discusses different methods of representing data in computers, including:
1. Binary representation of numbers using 0s and 1s. This allows integers and floating point numbers to be stored.
2. Text representation using character encoding standards like ASCII and Unicode which assign binary codes to letters, numbers and symbols.
3. Graphic representations including bitmapped images and vector graphics. Bitmaps store color values for each pixel while vectors store mathematical descriptions of shapes.
Binary units are used to measure digital data storage. The smallest unit is a bit which can have a value of 1 or 0. 8 bits make up a byte. 1024 bytes make up a kilobyte. Common units include kilobytes, megabytes, gigabytes, terabytes, petabytes, exabytes and zettabytes with each unit being 1024 times larger than the previous. Converting between units involves multiplication when going to smaller units and division when going to larger units.
- Decimal, binary, octal, and hexadecimal are different number systems used to represent numeric values.
- Decimal uses 10 digits (0-9), binary uses two digits (0-1), octal uses 8 digits (0-7), and hexadecimal uses 16 digits (0-9 and A-F).
- Each system has a base or radix - the number of unique digits used. Decimal is base 10, binary base 2, octal base 8, and hexadecimal base 16.
- Numbers can be converted between these systems using division and multiplication operations that take into account the place value of each digit based on the system's base.
This document provides an overview of data representation in computer systems. It discusses how computers use binary numeric codes to represent different types of data like text, numbers, graphics and audio. These codes allow computers to interpret raw sequences of 0s and 1s as meaningful information. The document then explains binary number systems in more detail, how decimal numbers can be converted to and from binary, and how bytes and bits are used to store data in computer memory and represent characters. Specific examples are given of how binary representations are used in applications like robotics to control devices.
This lesson is for students taking the Cambridge School certificate exams Computer science subject(2210).I hope that it will of help to students in this period of crisis. Send me your feedback or suggestions on buxooa72@ gmail.com,
This document discusses binary numbers and how they are used in computers. It explains that computers use base 2 binary numbers represented by 0s and 1s rather than base 10 numbers. It provides examples of converting between base 10 and base 2 numbers. It also defines units of measurement for binary numbers, with the basic unit being a byte which is 8 bits. Larger units include kilobytes, megabytes, gigabytes and terabytes.
- The document discusses direct mapped caches including cache hit/miss terminology and how direct mapped caches work by mapping each memory word to a single cache block based on the memory address.
- It provides an example of a direct mapped cache with 1024KB capacity and 32-bit addresses, showing the cache block format and how an example address would map to a cache block and tag field.
- The document also discusses cache block size being larger than one word to improve cache performance and provides an example with a 4-word cache block.
The document discusses different methods of representing data in computers, including:
1. Binary representation of numbers using 0s and 1s. This allows integers and floating point numbers to be stored.
2. Text representation using character encoding standards like ASCII and Unicode which assign binary codes to letters, numbers and symbols.
3. Graphic representations including bitmapped images and vector graphics. Bitmaps store color values for each pixel while vectors store mathematical descriptions of shapes.
Binary units are used to measure digital data storage. The smallest unit is a bit which can have a value of 1 or 0. 8 bits make up a byte. 1024 bytes make up a kilobyte. Common units include kilobytes, megabytes, gigabytes, terabytes, petabytes, exabytes and zettabytes with each unit being 1024 times larger than the previous. Converting between units involves multiplication when going to smaller units and division when going to larger units.
- Decimal, binary, octal, and hexadecimal are different number systems used to represent numeric values.
- Decimal uses 10 digits (0-9), binary uses two digits (0-1), octal uses 8 digits (0-7), and hexadecimal uses 16 digits (0-9 and A-F).
- Each system has a base or radix - the number of unique digits used. Decimal is base 10, binary base 2, octal base 8, and hexadecimal base 16.
- Numbers can be converted between these systems using division and multiplication operations that take into account the place value of each digit based on the system's base.
The document discusses different number systems including decimal, binary, octal, and hexadecimal. It explains how to represent numbers in these different bases and how to convert between them. The key techniques covered include multiplying place values to convert to and from decimal, grouping bits into sets of 3 or 4 to convert between binary and octal or hexadecimal, and using binary as an intermediate step to convert between non-binary bases. Examples are provided for adding, multiplying, and converting fractions between decimal and binary representations.
Lecture-2(2): Number System & ConversionMubashir Ali
This document provides an overview of different number systems including decimal, binary, octal, and hexadecimal. It discusses how each system uses a base (such as 10 for decimal, 2 for binary, 8 for octal, 16 for hexadecimal) and symbols (such as 0-9 for decimal and 0-1 for binary) to represent values. The key methods of converting between these number systems, such as repeated division and multiplying place values, are also explained through examples. Important concepts like bits, bytes, and representing binary patterns electrically in computers are covered.
This document discusses different number systems including positional and non-positional, and how to convert between decimal, binary, octal, and hexadecimal numbers. It explains that positional systems use the digit's position and value to determine its overall value, and different bases determine the maximum single digit value. Conversion between number systems involves representing values in their respective bases then performing arithmetic operations.
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
The document discusses binary units used to measure digital data storage. It defines common units like bits, bytes, kilobytes, megabytes, and provides examples of how much data each unit can store. It also shows how to convert between units using multiplication and division, as larger units are multiples of smaller units by powers of 1024.
This document discusses different number systems used in digital computers and their conversions. It begins with an introduction to digital number systems and then describes the decimal, binary, octal and hexadecimal number systems. It explains how to represent integers and real numbers in binary. The document also covers number conversions between these systems using different methods like repeated division. Finally, it discusses various ways of representing integers in binary like sign-magnitude, one's complement and two's complement representations.
The binary system is a base-2 number system that uses only two digits, 0 and 1. It is used by computers to represent data and instructions because digital electronics can only be in two states, on or off, which maps conveniently to the 1s and 0s of binary. In binary, each place value is a power of 2, so the decimal numbers can be converted to binary by determining whether they are greater or less than each power of 2 and writing the corresponding 1 or 0. This allows computers to perform calculations and logic using simple electronic switches corresponding to 1s and 0s in binary representations of numbers and instructions.
Bits are the basic units of information in computing representing either 1 or 0. 8 bits together form a byte, which can represent a single character. Common storage measurements are kilobytes (KB), megabytes (MB), gigabytes (GB), and terabytes (TB) which are powers of 1000 or 1024 bytes. A computer's processor understands information by interpreting patterns of transistors being on or off, with a transistor on representing 1 and off representing 0.
The document discusses computer number systems and data representation. It covers binary, octal, and hexadecimal number systems. It explains how computers use digital representation based on binary and how data is represented in memory as binary digits. It also discusses different data types, analog vs digital representation, and how various number systems are used to represent binary numbers.
This document discusses (2,4) trees, which are multi-way search trees where each internal node has between 2 and 4 children. It describes how (2,4) trees support efficient search, insertion, and deletion operations by allowing nodes to split or merge as needed to maintain the structure's balance, keeping the height of the tree at O(log n) and thus the time complexity of these operations at O(log n) as well. (2,4) trees lay the conceptual groundwork for red-black trees.
This document discusses measuring data in bits and bytes. It explains that a bit is the smallest unit of data a computer can understand, representing a 1 or 0. Eight bits make up a byte, which can represent a single character. Computer memory and storage are usually measured in kilobytes, megabytes, gigabytes, and larger units. The document also provides conversions between decimal, binary, and hexadecimal numbering systems and units of data storage.
1) A bit is the smallest unit of computer data and can have a value of 0 or 1. 8 bits form a byte.
2) Common units of computer data storage are the kilobyte (KB), megabyte (MB), gigabyte (GB), terabyte (TB), petabyte (PB), exabyte (EB), zettabyte (ZB), and yottabyte (YB), with each being 1024 times larger than the previous unit.
3) These units are used to measure and describe computer memory, storage, and data transmission speeds in bytes, kilobytes, megabytes etc. depending on the size of the data or storage being referred to
The document discusses the components inside a computer system unit. It describes how computers represent and store data, the components on the motherboard like the CPU and memory, and how the CPU processes instructions. It also outlines various connectors and ports on the exterior of the system unit that allow connection of peripheral devices.
This document discusses data representation and number systems in computing. It covers the following key points in 3 sentences:
Data such as numbers and coded information are represented using bits and bytes which can represent values, characters, or instructions. Common number systems used in computing include binary, decimal, octal, and hexadecimal, which use different radixes or bases to represent quantities with distinct symbols. Methods for converting between number systems involve grouping bits or digits into the appropriate radix and determining the place value of each position to arrive at the value in the target base.
Abstract
There is great research going on in the field of data security nowadays. Protecting information from disclosure and breach is of high importance to users personally and to organizations and businesses around the world, as most of information currently are sensitive electronic information transferred over the internet and stored in cloud based system. In this paper, we propose a method to increase the security of messages transferred on the internet, or information stored in the cloud. Our proposed method mainly relies on the Triple Data Encryption Standard (TDES) algorithm. TDES is intact the Data Encryption Standard repeated three times in succession to encrypt data. TDES is considered highly secure as there is no applicable method to break the code itself without knowing the key. We propose to encrypt the key using Cipher Feedback Block algorithm, before using TDES to encrypt data. Such that even when the key is disclosed, the key itself cannot decipher the ciphered text without enciphering the key with CFB. This introduces a new dimension of security to the TDES algorithm.
The method introduced in this paper increases the security of the TDES algorithm using CFB algorithm by increasing the key security, such that it is actually not possible to decipher the text without prior knowledge and agreement of key and algorithms used.
Keywords: Data Encryption Standard, Triple Data Encryption Algorithm, Cipher Feedback Block.
Modem = modulator + demodulator.
A modem is a device or program that enables a computer to transmit data over, for example, telephone or cable lines. Computer information is stored digitally, whereas information transmitted over telephone lines is transmitted in the form of analog waves.
Biometrics are automated methods of recognizing a person based on a physiological or behavioral characteristic. Among the features measured are face, fingerprints, hand geometry, handwriting, iris, retinal, vein, and voice. Biometric data are separate and distinct from personal information.
An inkjet printer works by spraying extremely small droplets of ink through nozzles onto paper to create an image. There are two main types of inkjet printers - thermal bubble printers that use heat to create ink bubbles and piezoelectric printers that use vibrations. When printing, the printer receives data from a computer, moves an print head assembly back and forth across the page while spraying ink droplets precisely, and advances the paper to print the entire image. Inkjet printers are inexpensive but manufacturers make their profits from ink cartridge sales.
A CGI program is any program designed to accept and return data that conforms to the CGI specification. The program could be written in any programming language, including C, Perl, Java, or Visual Basic.
This document provides an introduction to programming in Java by walking through how to set up a Java development environment and write a simple "Hello World" style program. It begins by outlining the assumptions and requirements, then guides the reader through downloading and installing the Java compiler. Next, it teaches some basic terminology and has the reader write, compile, and run a simple program that draws a diagonal line. The document explains what the program is doing line-by-line and encourages experimentation. It discusses where to find documentation on methods and classes to continue learning.
The document discusses different number systems including decimal, binary, octal, and hexadecimal. It explains how to represent numbers in these different bases and how to convert between them. The key techniques covered include multiplying place values to convert to and from decimal, grouping bits into sets of 3 or 4 to convert between binary and octal or hexadecimal, and using binary as an intermediate step to convert between non-binary bases. Examples are provided for adding, multiplying, and converting fractions between decimal and binary representations.
Lecture-2(2): Number System & ConversionMubashir Ali
This document provides an overview of different number systems including decimal, binary, octal, and hexadecimal. It discusses how each system uses a base (such as 10 for decimal, 2 for binary, 8 for octal, 16 for hexadecimal) and symbols (such as 0-9 for decimal and 0-1 for binary) to represent values. The key methods of converting between these number systems, such as repeated division and multiplying place values, are also explained through examples. Important concepts like bits, bytes, and representing binary patterns electrically in computers are covered.
This document discusses different number systems including positional and non-positional, and how to convert between decimal, binary, octal, and hexadecimal numbers. It explains that positional systems use the digit's position and value to determine its overall value, and different bases determine the maximum single digit value. Conversion between number systems involves representing values in their respective bases then performing arithmetic operations.
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
The document discusses binary units used to measure digital data storage. It defines common units like bits, bytes, kilobytes, megabytes, and provides examples of how much data each unit can store. It also shows how to convert between units using multiplication and division, as larger units are multiples of smaller units by powers of 1024.
This document discusses different number systems used in digital computers and their conversions. It begins with an introduction to digital number systems and then describes the decimal, binary, octal and hexadecimal number systems. It explains how to represent integers and real numbers in binary. The document also covers number conversions between these systems using different methods like repeated division. Finally, it discusses various ways of representing integers in binary like sign-magnitude, one's complement and two's complement representations.
The binary system is a base-2 number system that uses only two digits, 0 and 1. It is used by computers to represent data and instructions because digital electronics can only be in two states, on or off, which maps conveniently to the 1s and 0s of binary. In binary, each place value is a power of 2, so the decimal numbers can be converted to binary by determining whether they are greater or less than each power of 2 and writing the corresponding 1 or 0. This allows computers to perform calculations and logic using simple electronic switches corresponding to 1s and 0s in binary representations of numbers and instructions.
Bits are the basic units of information in computing representing either 1 or 0. 8 bits together form a byte, which can represent a single character. Common storage measurements are kilobytes (KB), megabytes (MB), gigabytes (GB), and terabytes (TB) which are powers of 1000 or 1024 bytes. A computer's processor understands information by interpreting patterns of transistors being on or off, with a transistor on representing 1 and off representing 0.
The document discusses computer number systems and data representation. It covers binary, octal, and hexadecimal number systems. It explains how computers use digital representation based on binary and how data is represented in memory as binary digits. It also discusses different data types, analog vs digital representation, and how various number systems are used to represent binary numbers.
This document discusses (2,4) trees, which are multi-way search trees where each internal node has between 2 and 4 children. It describes how (2,4) trees support efficient search, insertion, and deletion operations by allowing nodes to split or merge as needed to maintain the structure's balance, keeping the height of the tree at O(log n) and thus the time complexity of these operations at O(log n) as well. (2,4) trees lay the conceptual groundwork for red-black trees.
This document discusses measuring data in bits and bytes. It explains that a bit is the smallest unit of data a computer can understand, representing a 1 or 0. Eight bits make up a byte, which can represent a single character. Computer memory and storage are usually measured in kilobytes, megabytes, gigabytes, and larger units. The document also provides conversions between decimal, binary, and hexadecimal numbering systems and units of data storage.
1) A bit is the smallest unit of computer data and can have a value of 0 or 1. 8 bits form a byte.
2) Common units of computer data storage are the kilobyte (KB), megabyte (MB), gigabyte (GB), terabyte (TB), petabyte (PB), exabyte (EB), zettabyte (ZB), and yottabyte (YB), with each being 1024 times larger than the previous unit.
3) These units are used to measure and describe computer memory, storage, and data transmission speeds in bytes, kilobytes, megabytes etc. depending on the size of the data or storage being referred to
The document discusses the components inside a computer system unit. It describes how computers represent and store data, the components on the motherboard like the CPU and memory, and how the CPU processes instructions. It also outlines various connectors and ports on the exterior of the system unit that allow connection of peripheral devices.
This document discusses data representation and number systems in computing. It covers the following key points in 3 sentences:
Data such as numbers and coded information are represented using bits and bytes which can represent values, characters, or instructions. Common number systems used in computing include binary, decimal, octal, and hexadecimal, which use different radixes or bases to represent quantities with distinct symbols. Methods for converting between number systems involve grouping bits or digits into the appropriate radix and determining the place value of each position to arrive at the value in the target base.
Abstract
There is great research going on in the field of data security nowadays. Protecting information from disclosure and breach is of high importance to users personally and to organizations and businesses around the world, as most of information currently are sensitive electronic information transferred over the internet and stored in cloud based system. In this paper, we propose a method to increase the security of messages transferred on the internet, or information stored in the cloud. Our proposed method mainly relies on the Triple Data Encryption Standard (TDES) algorithm. TDES is intact the Data Encryption Standard repeated three times in succession to encrypt data. TDES is considered highly secure as there is no applicable method to break the code itself without knowing the key. We propose to encrypt the key using Cipher Feedback Block algorithm, before using TDES to encrypt data. Such that even when the key is disclosed, the key itself cannot decipher the ciphered text without enciphering the key with CFB. This introduces a new dimension of security to the TDES algorithm.
The method introduced in this paper increases the security of the TDES algorithm using CFB algorithm by increasing the key security, such that it is actually not possible to decipher the text without prior knowledge and agreement of key and algorithms used.
Keywords: Data Encryption Standard, Triple Data Encryption Algorithm, Cipher Feedback Block.
Modem = modulator + demodulator.
A modem is a device or program that enables a computer to transmit data over, for example, telephone or cable lines. Computer information is stored digitally, whereas information transmitted over telephone lines is transmitted in the form of analog waves.
Biometrics are automated methods of recognizing a person based on a physiological or behavioral characteristic. Among the features measured are face, fingerprints, hand geometry, handwriting, iris, retinal, vein, and voice. Biometric data are separate and distinct from personal information.
An inkjet printer works by spraying extremely small droplets of ink through nozzles onto paper to create an image. There are two main types of inkjet printers - thermal bubble printers that use heat to create ink bubbles and piezoelectric printers that use vibrations. When printing, the printer receives data from a computer, moves an print head assembly back and forth across the page while spraying ink droplets precisely, and advances the paper to print the entire image. Inkjet printers are inexpensive but manufacturers make their profits from ink cartridge sales.
A CGI program is any program designed to accept and return data that conforms to the CGI specification. The program could be written in any programming language, including C, Perl, Java, or Visual Basic.
This document provides an introduction to programming in Java by walking through how to set up a Java development environment and write a simple "Hello World" style program. It begins by outlining the assumptions and requirements, then guides the reader through downloading and installing the Java compiler. Next, it teaches some basic terminology and has the reader write, compile, and run a simple program that draws a diagonal line. The document explains what the program is doing line-by-line and encourages experimentation. It discusses where to find documentation on methods and classes to continue learning.
The document explains how domain name servers (DNS) work by translating human-readable domain names to machine-readable IP addresses. It discusses that DNS is a distributed database system with millions of name servers around the world administered by different organizations. When a domain name needs to be resolved to an IP address, the local name server is first queried, and if it doesn't have the answer, it will query other name servers in a recursive manner until the IP address is found.
CD burners allow users to record music and data files onto blank CDs. A CD burner uses a laser to burn tiny bumps onto the surface of a CD-R or CD-RW disc, encoding digital information. The laser moves outward from the center as the disc spins, burning a spiral track of data. CD-R discs can only be written to once, while CD-RW discs allow rewriting by erasing and rewriting sections through heating the disc material. Precise encoding and error-correction methods ensure the data can be read reliably on other players.
Banner ads are small rectangular advertisements that appear on web pages. When clicked, they link to an advertiser's website. They are usually simple HTML code that displays graphics and text. Advertisers hope users will click through to their site or remember their brand. Banner ad effectiveness is measured by click-throughs, page views, click-through rate, and cost per sale. Basic banner ads can be made by anyone, while professional designers offer more creative and attention-grabbing ads for a fee.
Mice translate hand motion into signals the computer understands using five main components: a ball that rolls when the mouse moves, rollers that detect motion, an encoding disk with holes, infrared LEDs and sensors that count pulses of light, and a processor chip. Modern optical mice use a camera to take 1500 pictures per second and detect pattern movement to determine cursor movement. Mice send data through connectors like PS/2 using a protocol that reports button states, direction of movement, and movement values in bytes sent 40 times per second.
CDs store large amounts of digital data by encoding it as microscopic bumps arranged in a continuous spiral track on the disc. A CD player precisely reads these bumps using a laser beam that detects changes in reflectivity. It tracks along the spiral from the inside to outside of the disc while adjusting the rotation speed to keep the data rate constant. Complex error-correcting encoding schemes are used to ensure reliable reading despite defects or errors.
This document provides an overview of how computer monitors work. It discusses the basics of display technology, including CRT vs LCD displays. When purchasing a monitor, factors to consider include display technology, resolution, refresh rate, color depth, aspect ratio, and power consumption. CRT displays were once dominant but are being replaced by thinner, less power-intensive LCD displays. The document provides details on concepts like dot pitch, aspect ratio, and how resolution is determined by factors like refresh rate and pixel density.
The document summarizes how 3D PC glasses work to provide a 3D viewing experience of games on a 2D monitor. It explains that the glasses block alternating views to each eye very quickly, tricking the brain into perceiving depth. Modern 3D glasses use LCD technology to block each eye's view synchronously with the images displayed, producing crystal clear 3D. The technology has advanced through several generations from modifying games to using graphics cards to handle the dual image processing. When buying glasses, compatibility with your graphics card and monitor type should be checked.
Computer data representation (integers, floating-point numbers, text, images,...ArtemKovera
This document discusses how computers represent different types of data at a low level. It covers binary, octal, and hexadecimal number systems. It also discusses how integers, floating point numbers, text, images, and sound are represented in computer memory in binary format using bits and bytes. Understanding how data is represented is important for programming efficiently and writing secure code.
In this ppt , you will learn about the evolution of number systems, decimal, binary and hexadecimal and why hexadecima is the most important form of number systems when working with microcontroller programming.
The document provides an overview of binary number systems and how they are used in computers. It begins by explaining that computers use binary rather than decimal. It then discusses:
1) How binary works by representing numbers as strings of 1s and 0s, with each digit representing a power of 2.
2) Methods for converting between binary and decimal numbers, including dividing decimal numbers by 2 repeatedly and expressing them as sums of powers of 2.
3) Key concepts like bits, bytes, and how all computer data is ultimately stored as binary.
The document discusses the binary number system used by computers. It begins by explaining how humans developed base-10 numbering based on having 10 fingers, but computers use base-2 binary numbering since transistors can only be on or off (1 or 0). All data in computers is represented as strings of 1s and 0s. It then provides examples of how binary numbers are written and converted to decimal numbers by treating each bit as a power of 2, similar to how decimal numbers treat each digit as a power of 10. Converting between binary and decimal involves writing the binary number as a sum of powers of 2 and adding the place values of bits that are 1.
Chapter 3-Data Representation in Computers.pptKalGetachew2
This document provides an overview of key topics related to computer data representation and binary number systems. It discusses how computers use binary switches to represent all data as strings of 0s and 1s. It also introduces different number systems like decimal, binary, octal and hexadecimal. The document explains how to convert between these number systems. Additionally, it covers binary arithmetic operations like addition, subtraction, multiplication and division. Finally, it discusses common units of data representation like bits, bytes and words, as well as coding methods such as BCD, EBCDIC and ASCII that are used to represent alphanumeric characters in binary.
This book's author is Zafar Ali Khan .
It consists of all the topics of As Level Computer Science topics that are required to be covered.
All credits goes to Zafar Ali Khan .
This document discusses various topics related to digital representation of data including:
1. The differences between FAT32 and NTFS file systems and their advantages and limitations.
2. How data is represented digitally using coding schemes like ASCII and converted between binary and other number systems.
3. An overview of different numbering systems including binary, decimal, octal and hexadecimal; and how to convert between them.
This document discusses various topics related to digital representation of data including:
1. The differences between FAT32 and NTFS file systems and their advantages and limitations.
2. How data is represented digitally using coding schemes like ASCII and converted between binary and other number systems.
3. An overview of different numbering systems including binary, decimal, octal and hexadecimal; and how to convert between them.
The document provides an overview of binary and decimal number systems. It begins by explaining that computers use binary while humans typically use decimal. It then discusses how binary represents numbers using only 1s and 0s, with each digit representing a power of 2. The document presents an example of counting coins in binary to illustrate this concept. It also discusses how to convert between binary and decimal numbers by writing the binary number as a sum of powers of 2 or repeatedly dividing the decimal number by 2 and recording the remainders as binary digits.
This document provides an overview of computing fundamentals including binary representation, data storage, and logic circuits. It discusses how binary numbers use the digits 0 and 1, how computers store this data using bits and bytes, and how logic gates like AND, OR, and NOT are used to perform calculations on binary numbers. Transistors are also introduced as the basic building block of logic circuits. The document aims to explain at a basic level how computers represent and manipulate information through binary encoding and logic operations.
This document summarizes a course on computing fundamentals. It discusses binary representation, how computers store data through binary encoding, and logic circuits that can process binary numbers. It explains how binary uses a base-2 system with the digits 0 and 1, and how this allows efficient electronic representation and processing of data. It also describes common logic gates like AND, OR, and NOT, and how more complex operations can be built by combining simple gates. Overall, the document provides a high-level introduction to basic computer concepts like binary, data storage, and logic operations.
This document discusses basic computer and information technology concepts. It introduces computer number systems including binary, decimal, octal and hexadecimal. It explains that computers use the binary number system and how bits and bytes are used to represent data. Examples are provided for converting between decimal, binary, octal and hexadecimal number systems.
This document provides an overview of the history of computing and how computers store data. It discusses:
- Gottfried Leibniz inventing binary arithmetic in the 17th century, which became the basis for how computers represent numbers.
- How early computers used mechanical switches to represent 1s and 0s, with switches in the on position representing 1 and off representing 0.
- Each byte in a computer's memory being divided into eight bits, with each bit representing a digit in the binary number system.
- Larger numbers being stored across multiple bytes, with the maximum value storable in a single byte being 255 and across two bytes being 65,535.
- A brief history of
Computers use binary, which is a base-2 counting system that uses only two digits: 0 and 1. A byte is made up of 8 bits, with each additional bit doubling the number of possible combinations from 2 to 256. Using 8 bits allows a byte to represent the 256 most common characters, including letters, numbers, and punctuation, when typed on a keyboard.
This slide show illustrates how bits are used in computers, both as content and to organize information in memory. The show also illustrates how we use hexadecimal as a convenient notation for binary information. And it illustrates how the number of bits relates to the number of values that may be represented and how to estimate this number quickly without a calculator.
By Don Mendonsa,
Professor of IT and CS
Tidewater Community College
There are two types of ciphers - Block and Stream. Block is used to .docxrelaine1
This document provides an overview of different modes of operation for ciphers including Electronic Code Book (ECB) mode, Cipher Block Chaining (CBC) mode, Output Feedback (OFB) mode, and Counter (CTR) mode. It explains the basic operations of each mode, such as how plaintext blocks are encrypted and how subsequent blocks depend on previous encrypted blocks. Weaknesses of the DES cipher are also discussed, noting it was withdrawn in 2005 due to insufficient security. The document then provides an example of applying CBC mode to DES encryption.
The document discusses how computers represent data using binary numbers (1s and 0s). It explains that binary is used because it provides an easy way to represent two states (on/off) in storage devices. It then discusses how different numbers of bits (binary digits) can be used to represent different numbers in binary, and provides examples of converting between binary and decimal numbers. Finally, it briefly introduces the concept of data compression for reducing the size of files.
Number System, Conversion, Decimal to Binary, Decimal to Octal, Decimal to Binary, Decimal to HexaDecimal, Binary to Decimal, Octal to Decimal, Hexadecimal to Decimal, Binary to Octal, Binary to Hexadecimal, Octal to Hexadecimal, BCD, Binary Addition
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1. How Bits and Bytes Work
by Marshall Brain
If you have used a computer for more than five
minutes, then you have heard the words bits and
bytes. Both RAM and hard disk capacities are
measured in bytes, as are file sizes when you
examine them in a file viewer.
You might hear an advertisement that says, "This
computer has a 32-bit Pentium processor with 64
megabytes of RAM and 2.1 gigabytes of hard
disk space." And many HowStuffWorks articles
talk about bytes (for example, How CDs Work). In
this article, we will discuss bits and bytes so that
you have a complete understanding.
Decimal Numbers
The easiest way to understand bits is to compare them to something you know: digits. A digit is a
single place that can hold numerical values between 0 and 9. Digits are normally combined
together in groups to create larger numbers. For example, 6,357 has four digits. It is understood
that in the number 6,357, the 7 is filling the "1s place," while the 5 is filling the 10s place, the 3 is
filling the 100s place and the 6 is filling the 1,000s place. So you could express things this way if
you wanted to be explicit:
(6 * 1000) + (3 * 100) + (5 * 10) + (7 * 1) = 6000 + 300 + 50 + 7 = 6357
Another way to express it would be to use powers of 10. Assuming that we are going to
represent the concept of "raised to the power of" with the "^" symbol (so "10 squared" is written
as "10^2"), another way to express it is like this:
(6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357
What you can see from this expression is that each digit is a placeholder for the next higher
power of 10, starting in the first digit with 10 raised to the power of zero.
That should all feel pretty comfortable -- we work with decimal digits every day. The neat thing
about number systems is that there is nothing that forces you to have 10 different values in a
digit. Our base-10 number system likely grew up because we have 10 fingers, but if we
happened to evolve to have eight fingers instead, we would probably have a base-8 number
system. You can have base-anything number systems. In fact, there are lots of good reasons to
use different bases in different situations.
Bits
Computers happen to operate using the base-2 number system, also known as the binary
number system (just like the base-10 number system is known as the decimal number system).
The reason computers use the base-2 system is because it makes it a lot easier to implement
them with current electronic technology. You could wire up and build computers that operate in
base-10, but they would be fiendishly expensive right now. On the other hand, base-2 computers
are relatively cheap.
So computers use binary numbers, and therefore use binary digits in place of decimal digits.
The word bit is a shortening of the words "Binary digIT." Whereas decimal digits have 10 possible
values ranging from 0 to 9, bits have only two possible values: 0 and 1. Therefore, a binary
number is composed of only 0s and 1s, like this: 1011. How do you figure out what the value of
2. the binary number 1011 is? You do it in the same way we did it above for 6357, but you use a
base of 2 instead of a base of 10. So:
(1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11
You can see that in binary numbers, each bit holds the value of increasing powers of 2. That
makes counting in binary pretty easy. Starting at zero and going through 20, counting in decimal
and binary looks like this:
0 = 0
1 = 1
2 = 10
3 = 11
4 = 100
5 = 101
6 = 110
7 = 111
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111
16 = 10000
17 = 10001
18 = 10010
19 = 10011
20 = 10100
When you look at this sequence, 0 and 1 are the same for decimal and binary number systems.
At the number 2, you see carrying first take place in the binary system. If a bit is 1, and you add 1
to it, the bit becomes 0 and the next bit becomes 1. In the transition from 15 to 16 this effect roles
over through 4 bits, turning 1111 into 10000.
Bytes
Bits are rarely seen alone in computers. They are almost always bundled together into 8-bit
collections, and these collections are called bytes. Why are there 8 bits in a byte? A similar
question is, "Why are there 12 eggs in a dozen?" The 8-bit byte is something that people settled
on through trial and error over the past 50 years.
With 8 bits in a byte, you can represent 256 values ranging from 0 to 255, as shown here:
0 = 00000000
1 = 00000001
2 = 00000010
...
254 = 11111110
255 = 11111111
In the article How CDs Work, you learn that a CD uses 2 bytes, or 16 bits, per sample. That gives
each sample a range from 0 to 65,535, like this:
0 = 0000000000000000
1 = 0000000000000001
2 = 0000000000000010
...
65534 = 1111111111111110
65535 = 1111111111111111
3. Bytes are frequently used to hold individual characters in a text document. In the ASCII
character set, each binary value between 0 and 127 is given a specific character. Most
computers extend the ASCII character set to use the full range of 256 characters available in a
byte. The upper 128 characters handle special things like accented characters from common
foreign languages.
You can see the 127 standard ASCII codes below. Computers store text documents, both on disk
and in memory, using these codes. For example, if you use Notepad in Windows 95/98 to create
a text file containing the words, "Four score and seven years ago," Notepad would use 1 byte of
memory per character (including 1 byte for each space character between the words -- ASCII
character 32). When Notepad stores the sentence in a file on disk, the file will also contain 1 byte
per character and per space.
Try this experiment: Open up a new file in Notepad and insert the sentence, "Four score and
seven years ago" in it. Save the file to disk under the name getty.txt. Then use the explorer and
look at the size of the file. You will find that the file has a size of 30 bytes on disk: 1 byte for each
character. If you add another word to the end of the sentence and re-save it, the file size will jump
to the appropriate number of bytes. Each character consumes a byte.
If you were to look at the file as a computer looks at it, you would find that each byte contains not
a letter but a number -- the number is the ASCII code corresponding to the character (see below).
So on disk, the numbers for the file look like this:
F o u r a n d s e v e n
70 111 117 114 32 97 110 100 32 115 101 118 101 110
By looking in the ASCII table, you can see a one-to-one correspondence between each character
and the ASCII code used. Note the use of 32 for a space -- 32 is the ASCII code for a space. We
could expand these decimal numbers out to binary numbers (so 32 = 00100000) if we wanted to
be technically correct -- that is how the computer really deals with things.
Standard ASCII Character Set
The first 32 values (0 through 31) are codes for things like carriage return and line feed. The
space character is the 33rd value, followed by punctuation, digits, uppercase characters and
lowercase characters.
0 NUL
1 SOH
2 STX
3 ETX
4 EOT
5 ENQ
6 ACK
7 BEL
8 BS
9 TAB
10 LF
11 VT
12 FF
13 CR
14 SO
15 SI
16 DLE
17 DC1
18 DC2
19 DC3
20 DC4
21 NAK
4. 22 SYN
23 ETB
24 CAN
25 EM
26 SUB
27 ESC
28 FS
29 GS
30 RS
31 US
32
33 !
34 "
35 #
36 $
37 %
38 &
39 '
40 (
41 )
42 *
43 +
44 ,
45 -
46 .
47 /
48 0
49 1
50 2
51 3
52 4
53 5
54 6
55 7
56 8
57 9
58 :
59 ;
60 <
61 =
62 >
63 ?
64 @
65 A
66 B
67 C
68 D
69 E
70 F
71 G
72 H
73 I
74 J
75 K
76 L
77 M
78 N
79 O
80 P
81 Q
82 R
5. 83 S
84 T
85 U
86 V
87 W
88 X
89 Y
90 Z
91 [
92
93 ]
94 ^
95 _
96 `
97 a
98 b
99 c
100 d
101 e
102 f
103 g
104 h
105 i
106 j
107 k
108 l
109 m
110 n
111 o
112 p
113 q
114 r
115 s
116 t
117 u
118 v
119 w
120 x
121 y
122 z
123 {
124 |
125 }
126 ~
127 DEL
Lots of Bytes
When you start talking about lots of bytes, you get into prefixes like kilo, mega and giga, as in
kilobyte, megabyte and gigabyte (also shortened to K, M and G, as in Kbytes, Mbytes and Gbytes
or KB, MB and GB). The following table shows the multipliers:
Name Abbr. Size
Kilo K 2^10 = 1,024
Mega M 2^20 = 1,048,576
Giga G 2^30 = 1,073,741,824
Tera T 2^40 = 1,099,511,627,776
Peta P 2^50 = 1,125,899,906,842,624
6. Exa E 2^60 = 1,152,921,504,606,846,976
Zetta Z 2^70 = 1,180,591,620,717,411,303,424
Yotta Y 2^80 = 1,208,925,819,614,629,174,706,176
You can see in this chart that kilo is about a thousand, mega is about a million, giga is about a
billion, and so on. So when someone says, "This computer has a 2 gig hard drive," what he or
she means is that the hard drive stores 2 gigabytes, or approximately 2 billion bytes, or exactly
2,147,483,648 bytes. How could you possibly need 2 gigabytes of space? When you consider
that one CD holds 650 megabytes, you can see that just three CDs worth of data will fill the whole
thing! Terabyte databases are fairly common these days, and there are probably a few petabyte
databases floating around the Pentagon by now.
Binary Math
Binary math works just like decimal math, except that the value of each bit can be only 0 or 1. To
get a feel for binary math, let's start with decimal addition and see how it works. Assume that we
want to add 452 and 751:
452
+ 751
---
1203
To add these two numbers together, you start at the right: 2 + 1 = 3. No problem. Next, 5 + 5 =
10, so you save the zero and carry the 1 over to the next place. Next, 4 + 7 + 1 (because of the
carry) = 12, so you save the 2 and carry the 1. Finally, 0 + 0 + 1 = 1. So the answer is 1203.
Binary addition works exactly the same way:
010
+ 111
---
1001
Starting at the right, 0 + 1 = 1 for the first digit. No carrying there. You've got 1 + 1 = 10 for the
second digit, so save the 0 and carry the 1. For the third digit, 0 + 1 + 1 = 10, so save the zero
and carry the 1. For the last digit, 0 + 0 + 1 = 1. So the answer is 1001. If you translate everything
over to decimal you can see it is correct: 2 + 7 = 9.
To see how boolean addition is implemented using gates, see How Boolean Logic Works.
Quick Recap
• Bits are binary digits. A bit can hold the value 0 or 1.
• Bytes are made up of 8 bits each.
• Binary math works just like decimal math, but each bit can have a value of only 0 or 1.
There really is nothing more to it -- bits and bytes are that simple!