This document discusses number representation systems used in computers, including binary, decimal, octal, and hexadecimal. It provides examples of converting between these different bases. Specifically, it covers:
1) Converting between decimal, binary, octal, and hexadecimal using positional notation and place values.
2) Representing signed integers in binary using ones' complement and twos' complement notation.
3) Tables for converting binary numbers to octal and hexadecimal using place values of each base.
4) Examples of converting values between the different number bases both manually and using the provided conversion tables.
This document contains examples and problems related to binary number systems. It begins by listing octal, hexadecimal, and base-12 numbers and converting between number systems. Later problems involve operations like addition, subtraction, multiplication and division using binary, octal and hexadecimal numbers. Conversions between decimal, binary, octal and hexadecimal are demonstrated. Complement representations for signed binary numbers are also covered.
This document summarizes different number systems used in computing including binary, octal, decimal, and hexadecimal. It explains how to convert between these number systems using theorems about their bases. Key topics covered include binary arithmetic, signed and unsigned integer representation, and how floating point numbers and characters are stored in binary format. Conversion charts are provided for binary to octal and hexadecimal. Representations of integers, characters, and floating point numbers in binary are also summarized.
The document discusses different number systems used in computing, including binary, hexadecimal, and octal. It explains that computers internally use the binary number system to represent data and perform calculations. Hexadecimal provides a shorthand way to work with binary numbers, with each hex digit corresponding to four binary digits. The document also covers how to convert between decimal, binary, hexadecimal, and octal numbers. It provides examples of expanding numbers in different bases, as well as adding and subtracting binary numbers using complements.
Digital and Logic Design Chapter 1 binary_systemsImran Waris
This document discusses binary number systems and digital computing. It covers binary numbers, number base conversions between decimal, binary, octal and hexadecimal. It also discusses binary coding techniques like binary-coded decimal, signed magnitude representation, one's complement and two's complement representations for negative numbers.
This document introduces basic concepts of digital electronics. It discusses that digital electronics deals with binary numbers (0 and 1). It also covers number systems like binary, octal, decimal, and hexadecimal. Finally, it demonstrates different methods of number conversion between these systems - such as decimal to binary, binary to decimal, and converting between different bases like hexadecimal to octal. Conversions are performed by dividing or multiplying by the base and writing the remainders in reverse order.
The document discusses different number systems used to represent numeric values in computers, including binary, octal, hexadecimal, and decimal. It provides examples of converting between these number systems using techniques like repeated division and multiplying digits by their place values. Character encoding schemes like ASCII, EBCDIC, and Unicode are also covered, explaining how they allow computers to represent letters, punctuation, and other characters with binary values.
To convert a binary number to octal:
1) Separate the binary number into groups of 3 digits from the right.
2) Convert each 3-digit group to its octal equivalent.
3) The octal number is the combination of each converted group from right to left.
The document discusses different number systems including positional and non-positional systems. It covers the decimal, binary, octal and hexadecimal number systems in detail. Key points include:
1) Positional systems use the place value of digits to represent numbers, with the decimal and binary systems being examples.
2) Converting between number bases involves repeatedly dividing the number by the new base and recording the remainders as digits.
3) Binary, octal and hexadecimal use groups of bits/digits to simplify conversions between the bases.
4) Floating point numbers represent real numbers with a mantissa and exponent in positional notation.
This document contains examples and problems related to binary number systems. It begins by listing octal, hexadecimal, and base-12 numbers and converting between number systems. Later problems involve operations like addition, subtraction, multiplication and division using binary, octal and hexadecimal numbers. Conversions between decimal, binary, octal and hexadecimal are demonstrated. Complement representations for signed binary numbers are also covered.
This document summarizes different number systems used in computing including binary, octal, decimal, and hexadecimal. It explains how to convert between these number systems using theorems about their bases. Key topics covered include binary arithmetic, signed and unsigned integer representation, and how floating point numbers and characters are stored in binary format. Conversion charts are provided for binary to octal and hexadecimal. Representations of integers, characters, and floating point numbers in binary are also summarized.
The document discusses different number systems used in computing, including binary, hexadecimal, and octal. It explains that computers internally use the binary number system to represent data and perform calculations. Hexadecimal provides a shorthand way to work with binary numbers, with each hex digit corresponding to four binary digits. The document also covers how to convert between decimal, binary, hexadecimal, and octal numbers. It provides examples of expanding numbers in different bases, as well as adding and subtracting binary numbers using complements.
Digital and Logic Design Chapter 1 binary_systemsImran Waris
This document discusses binary number systems and digital computing. It covers binary numbers, number base conversions between decimal, binary, octal and hexadecimal. It also discusses binary coding techniques like binary-coded decimal, signed magnitude representation, one's complement and two's complement representations for negative numbers.
This document introduces basic concepts of digital electronics. It discusses that digital electronics deals with binary numbers (0 and 1). It also covers number systems like binary, octal, decimal, and hexadecimal. Finally, it demonstrates different methods of number conversion between these systems - such as decimal to binary, binary to decimal, and converting between different bases like hexadecimal to octal. Conversions are performed by dividing or multiplying by the base and writing the remainders in reverse order.
The document discusses different number systems used to represent numeric values in computers, including binary, octal, hexadecimal, and decimal. It provides examples of converting between these number systems using techniques like repeated division and multiplying digits by their place values. Character encoding schemes like ASCII, EBCDIC, and Unicode are also covered, explaining how they allow computers to represent letters, punctuation, and other characters with binary values.
To convert a binary number to octal:
1) Separate the binary number into groups of 3 digits from the right.
2) Convert each 3-digit group to its octal equivalent.
3) The octal number is the combination of each converted group from right to left.
The document discusses different number systems including positional and non-positional systems. It covers the decimal, binary, octal and hexadecimal number systems in detail. Key points include:
1) Positional systems use the place value of digits to represent numbers, with the decimal and binary systems being examples.
2) Converting between number bases involves repeatedly dividing the number by the new base and recording the remainders as digits.
3) Binary, octal and hexadecimal use groups of bits/digits to simplify conversions between the bases.
4) Floating point numbers represent real numbers with a mantissa and exponent in positional notation.
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 discusses number systems and conversions between different bases. It explains that computers use the binary system with bits representing 0s and 1s. 8 bits form a byte. Decimal, binary, octal and hexadecimal numbering systems are covered. Methods for converting between these bases are provided using division and remainders or grouping bits. Common powers and units used in computing like kilo, mega and giga are also defined. Exercises on converting values between the different number systems are included.
This document discusses data representation and number systems in computers. It covers binary, octal, decimal, and hexadecimal number systems. Key points include:
- Data in computers is represented using binary numbers and different number systems allow for more efficient representations.
- Converting between number systems like binary, octal, decimal, and hexadecimal is explained through examples of dividing numbers and grouping bits.
- Signed numbers can be represented using complement representations like one's complement and two's complement, with subtraction implemented through addition of complements. Fast methods for calculating two's complement are described.
There are several number systems that can be used to represent numbers, which can be categorized as positional or non-positional. Commonly used positional systems include decimal, binary, octal, and hexadecimal. Different systems use different bases and symbols to represent values. Numbers can be converted between systems using techniques like successive division, weighted multiplication, or grouping bits. Understanding different number systems is important for both humans and computers.
This document contains slides for a lecture on digital logic design. It introduces the topic and provides an outline of contents to be covered, including number systems, function minimization methods, combinational and sequential systems, and hardware design languages. It also lists the speaker's contact details and information about textbook references, grading policies, and acknowledgments. The first chapter focuses on number systems, covering binary, decimal, octal, and hexadecimal representation, addition, subtraction, signed numbers, binary-coded decimal, and other coding systems. Examples of converting between different bases are provided.
The document discusses binary number representation and arithmetic. It explains decimal to binary conversion. It also describes signed number representation using sign-magnitude and one's complement and two's complement methods. The key advantages of two's complement are that addition can be performed using the same method for positive and negative numbers. Subtraction using two's complement is performed by adding the number to the complement of the subtrahend. Examples of binary addition and subtraction are provided to illustrate these concepts.
The document provides information about computer arithmetic and binary number representation. It discusses addition and subtraction in binary, signed and unsigned numbers, overflow, and multiplication algorithms. It explains how binary addition and subtraction work using bit-by-bit operations. For multiplication, it describes the shift-add algorithm where the multiplicand is shifted and added to the product based on the multiplier bits. Hardware for implementing this algorithm with registers is also shown.
Chapter 07 Digital Alrithmetic and Arithmetic CircuitsSSE_AndyLi
This document discusses digital arithmetic and arithmetic circuits. It covers topics such as signed and unsigned binary numbers, addition, subtraction, overflow, binary-coded decimal codes, and the implementation of adders using full adders in VHDL. Specifically, it defines common digital arithmetic concepts like carries, sums, overflow, and binary number representations. It also describes half adders, full adders, ripple carry adders, and how to construct multi-bit adders using full adder components in VHDL.
This document discusses different number systems including non-positional, positional, decimal, binary, octal, and hexadecimal systems. It provides examples of how to convert numbers between these bases using direct conversion methods or shortcuts. Key aspects covered include how the position and base of each digit determines its value in a number, converting a number to decimal and then to another base, and dividing binary, octal, or hexadecimal numbers into groups to convert to a different base number system.
Number System | Types of Number System | Binary Number System | Octal Number ...Get & Spread Knowledge
Topic: Number System | Types of Number System | Binary Number System | Octal Number System | Decimal Number System | Hexadecimal Number System
Subject: Digital Logic & Design
Programs: Bachelor of Computer Science, Bachelor of Engineering, Bachelor of Technology, Bachelor of IT, Master of Computer Science.
Lecturer: Junaid Qamar
Email: Getandspreadknowledge@gmail.com
The document discusses different number systems including binary, decimal, hexadecimal, and octal. It explains that number systems have a base, which is the number of unique digits used, and provides examples of how to convert between number systems. Binary coded decimal is also introduced as a way to efficiently store decimal numbers using a binary representation where each decimal digit is stored in 4 bits. Algorithms for binary addition and logic gates are briefly covered.
Digital systems represent information using discrete binary values of 0 and 1 rather than continuous analog values. Binary numbers use a base-2 numbering system with place values that are powers of 2. There are various number systems like decimal, binary, octal and hexadecimal that use different number bases and represent the same number in different ways. Complements are used in binary arithmetic to perform subtraction by adding the 1's or 2's complement of a number. The 1's complement is obtained by inverting all bits, while the 2's complement is obtained by inverting all bits and adding 1.
- The document discusses number systems and bases, including binary, decimal, octal, and hexadecimal.
- It explains positional notation and how numbers are represented in different bases using place values that are powers of the base.
- The range of numbers that can be represented depends on the base and number of digits used. More digits allow larger numbers to be represented.
This document discusses different types of breakfasts from around the world. It begins by introducing continental breakfast, which consists of lighter options like breads, jams, fruits and coffee. American breakfast is described as involving cereals, breads, eggs and beverages. English breakfast is noted as a more substantial meal including eggs, meats, fish and tea or coffee. South Indian breakfast includes items like idli and dosa while north Indian breakfast features breads, curds and sweets. Sample menus are provided for some breakfast types.
This document contains notes from research conducted on October 17th, 2014 on various items related to a radio broadcast program. It notes the source of information for 4 items was secondary research conducted online, covering the broadcast time, number of songs per hour, and target age group. The 5th item involved primary research through a questionnaire to gather opinions on what people think of the radio broadcast.
The document discusses 10 latest trends in email marketing, including the growing importance of mobile email and responsive design, changes to Gmail like image caching and tabs, new products like Google Inbox, legal issues like Canada's Anti-Spam Legislation (CASL), and opportunities for personalization, monetization, onboarding new subscribers, and integrating email with social media. The presentation was given by George DiGuido, Head of Email Marketing at About.com, to discuss strategies and best practices for leveraging new developments in digital marketing.
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 discusses number systems and conversions between different bases. It explains that computers use the binary system with bits representing 0s and 1s. 8 bits form a byte. Decimal, binary, octal and hexadecimal numbering systems are covered. Methods for converting between these bases are provided using division and remainders or grouping bits. Common powers and units used in computing like kilo, mega and giga are also defined. Exercises on converting values between the different number systems are included.
This document discusses data representation and number systems in computers. It covers binary, octal, decimal, and hexadecimal number systems. Key points include:
- Data in computers is represented using binary numbers and different number systems allow for more efficient representations.
- Converting between number systems like binary, octal, decimal, and hexadecimal is explained through examples of dividing numbers and grouping bits.
- Signed numbers can be represented using complement representations like one's complement and two's complement, with subtraction implemented through addition of complements. Fast methods for calculating two's complement are described.
There are several number systems that can be used to represent numbers, which can be categorized as positional or non-positional. Commonly used positional systems include decimal, binary, octal, and hexadecimal. Different systems use different bases and symbols to represent values. Numbers can be converted between systems using techniques like successive division, weighted multiplication, or grouping bits. Understanding different number systems is important for both humans and computers.
This document contains slides for a lecture on digital logic design. It introduces the topic and provides an outline of contents to be covered, including number systems, function minimization methods, combinational and sequential systems, and hardware design languages. It also lists the speaker's contact details and information about textbook references, grading policies, and acknowledgments. The first chapter focuses on number systems, covering binary, decimal, octal, and hexadecimal representation, addition, subtraction, signed numbers, binary-coded decimal, and other coding systems. Examples of converting between different bases are provided.
The document discusses binary number representation and arithmetic. It explains decimal to binary conversion. It also describes signed number representation using sign-magnitude and one's complement and two's complement methods. The key advantages of two's complement are that addition can be performed using the same method for positive and negative numbers. Subtraction using two's complement is performed by adding the number to the complement of the subtrahend. Examples of binary addition and subtraction are provided to illustrate these concepts.
The document provides information about computer arithmetic and binary number representation. It discusses addition and subtraction in binary, signed and unsigned numbers, overflow, and multiplication algorithms. It explains how binary addition and subtraction work using bit-by-bit operations. For multiplication, it describes the shift-add algorithm where the multiplicand is shifted and added to the product based on the multiplier bits. Hardware for implementing this algorithm with registers is also shown.
Chapter 07 Digital Alrithmetic and Arithmetic CircuitsSSE_AndyLi
This document discusses digital arithmetic and arithmetic circuits. It covers topics such as signed and unsigned binary numbers, addition, subtraction, overflow, binary-coded decimal codes, and the implementation of adders using full adders in VHDL. Specifically, it defines common digital arithmetic concepts like carries, sums, overflow, and binary number representations. It also describes half adders, full adders, ripple carry adders, and how to construct multi-bit adders using full adder components in VHDL.
This document discusses different number systems including non-positional, positional, decimal, binary, octal, and hexadecimal systems. It provides examples of how to convert numbers between these bases using direct conversion methods or shortcuts. Key aspects covered include how the position and base of each digit determines its value in a number, converting a number to decimal and then to another base, and dividing binary, octal, or hexadecimal numbers into groups to convert to a different base number system.
Number System | Types of Number System | Binary Number System | Octal Number ...Get & Spread Knowledge
Topic: Number System | Types of Number System | Binary Number System | Octal Number System | Decimal Number System | Hexadecimal Number System
Subject: Digital Logic & Design
Programs: Bachelor of Computer Science, Bachelor of Engineering, Bachelor of Technology, Bachelor of IT, Master of Computer Science.
Lecturer: Junaid Qamar
Email: Getandspreadknowledge@gmail.com
The document discusses different number systems including binary, decimal, hexadecimal, and octal. It explains that number systems have a base, which is the number of unique digits used, and provides examples of how to convert between number systems. Binary coded decimal is also introduced as a way to efficiently store decimal numbers using a binary representation where each decimal digit is stored in 4 bits. Algorithms for binary addition and logic gates are briefly covered.
Digital systems represent information using discrete binary values of 0 and 1 rather than continuous analog values. Binary numbers use a base-2 numbering system with place values that are powers of 2. There are various number systems like decimal, binary, octal and hexadecimal that use different number bases and represent the same number in different ways. Complements are used in binary arithmetic to perform subtraction by adding the 1's or 2's complement of a number. The 1's complement is obtained by inverting all bits, while the 2's complement is obtained by inverting all bits and adding 1.
- The document discusses number systems and bases, including binary, decimal, octal, and hexadecimal.
- It explains positional notation and how numbers are represented in different bases using place values that are powers of the base.
- The range of numbers that can be represented depends on the base and number of digits used. More digits allow larger numbers to be represented.
This document discusses different types of breakfasts from around the world. It begins by introducing continental breakfast, which consists of lighter options like breads, jams, fruits and coffee. American breakfast is described as involving cereals, breads, eggs and beverages. English breakfast is noted as a more substantial meal including eggs, meats, fish and tea or coffee. South Indian breakfast includes items like idli and dosa while north Indian breakfast features breads, curds and sweets. Sample menus are provided for some breakfast types.
This document contains notes from research conducted on October 17th, 2014 on various items related to a radio broadcast program. It notes the source of information for 4 items was secondary research conducted online, covering the broadcast time, number of songs per hour, and target age group. The 5th item involved primary research through a questionnaire to gather opinions on what people think of the radio broadcast.
The document discusses 10 latest trends in email marketing, including the growing importance of mobile email and responsive design, changes to Gmail like image caching and tabs, new products like Google Inbox, legal issues like Canada's Anti-Spam Legislation (CASL), and opportunities for personalization, monetization, onboarding new subscribers, and integrating email with social media. The presentation was given by George DiGuido, Head of Email Marketing at About.com, to discuss strategies and best practices for leveraging new developments in digital marketing.
This document lists scientific and technical publications by Nirmal Babu K and others, including 11 research or review articles and chapters in books on topics related to micropropagation and biotechnology of spices. Specifically, it discusses micropropagation of various spice crops like camphor tree, long pepper, large cardamom; the role of plant biotechnology in improvement and genetic conservation of spices; and production of synthetic seeds in some spice crops.
The document discusses several plants from the mint family that are popular in herb gardens:
- Mentha includes varieties like spearmint and peppermint that are used widely in cooking and repel pests, though they can be invasive.
- Basilicum refers to basil, which is a key ingredient in Italian cooking and comes in flavors like sweet, Thai, orange and lemon.
- Lavendula is lavender, which is grown for its relaxing scent in products like soap and perfume.
- Hyssopus has a bitter flavor but was used in ancient Greece and the Bible for purification rituals.
- Salvia includes ornamental varieties and the kitchen herb sage, which is also used in incense and
This document provides guidance on managing a 21st century classroom. It discusses using a back channel for student conversations during lessons. It emphasizes setting clear expectations for technology use, establishing consistent rules and procedures, and using progressive discipline. It also stresses the importance of instructional design principles like backwards planning and constructivism when integrating technology. The document provides checklists and tips for communication, lesson planning, and getting classroom management and technology use organized for the school year.
This document provides an overview of key concepts for studying history, including:
1) History is the study of the past using evidence to understand what happened and why. Historians sequence events and interpret sources to draw conclusions.
2) The Gregorian calendar system established a standardized way to date historical events using the BC/BCE and AD/CE eras.
3) Historians use primary sources created during the time being studied, as well as secondary sources like books, to investigate the past from different perspectives. Primary sources include written documents, images, artifacts, and oral histories.
The document proposes a new system to address sexual harassment of women on university campuses. It summarizes survey results that found high rates of verbal and physical harassment at some Indian universities. It then outlines a three-part solution involving preventative measures like CCTV cameras, educational workshops, and establishing a Women's Grievance Cell with student and faculty representation to efficiently handle harassment complaints and ensure swift action against offenders. Challenges to the system and mitigation strategies are also discussed.
Justice in Time: applying TOC to the law courts system in Israel - Shimeon Pa...commonsenseLT
Shimeon Pass, expert in Value Enhancement and implementation of advanced management concepts (Israel) @ @ TOCICO International Public Sector Effectiveness Conference 2013 Vilnius
- Eliminating judges' wasted time and the complete kit concept.
- Continuous hearing of evidence sessions.
- Can a case be approached as a project?
- Is 'fair' distribution of dossiers among judges really effective?
- Written or oral summations?
- How 'long' should the verdict document be?
- The role of legal aides.
- Controlled release of dossiers to the judges by the double Drum-Buffer-Rope (dDBR) mechanism.
More information - http://pse.lt
The document discusses the history of globalization in three periods:
1. Earliest forms/Archaic Globalization from the 1600s characterized by increased trade links and cultural exchange between states and empires along major trade routes like the Silk Road. This led to developments in cartography, travel, and the dissemination of knowledge.
2. Protoglobalization from 1600-1800 saw a shift to trading commodities and conflicts between expanding western European nations. This included the rise of the Atlantic slave trade and colonialism, increasing global disease, and new technologies.
3. Modern Globalization from 1800 to present, fueled by the Industrial Revolution. Key developments included the Bretton Woods
SharePoint Governance - No one should carry the burden aloneBenjamin Niaulin
Building a SharePoint Governance is often complicated and complex. In this presentation I showed that it can and should be made out to be simple. With contextual Wiki pages instead of heavy PDFs it can provide a helpful SharePoint Governance to your users.
In fact, the key word to take away is "Guideline" and not policing SharePoint. Helping people use the platform correctly with Governance.
This document appears to be an English language exam with multiple sections testing grammar, vocabulary, and reading comprehension. It includes questions about:
1. Completing sentences in the present simple and continuous tenses.
2. Conjugating verbs into the past simple and past continuous tenses.
3. Matching vocabulary words with definitions.
4. Answering comprehension questions about a short passage of text.
The document contains a variety of grammar, vocabulary, and reading exercises for students to demonstrate their English language skills.
La Biennale de Dakar comme projet de coopération et de développement, Soutena...Iolanda Pensa
La Biennale de Dakar
comme projet de coopération et de développement. Candidat Iolanda Pensa
Directeurs de recherche Jean-Loup Amselle en cotutelle avec Rossella Salerno
Jury Jean-Loup Amselle, Elio Grazioli, Rossella Salerno, Tobias Wendl
Paris, 27 juin 2011
Ecole des Hautes Etudes en Sciences Sociales
en cotutelle avec Politecnico di Milano, Dipartimento di Architettura e Pianificazione
Thèse de doctorat en
Anthropologie sociale et ethnologie
Governo e progettazione del territorio
Iolanda Pensa (nom complet Maria Iolanda Isabella Pensa), La Biennale de Dakar comme projet de coopération et de développement, thèse de doctorat en Anthropologie sociale et ethnologie et en Governo e progettazione del territorio, Ecole des Hautes Etudes en Sciences Sociales en cotutelle avec Politecnico di Milano, Dipartimento di Architettura e Pianificazione, directeurs de recherche Jean-Loup Amselle en cotutelle avec Rossella Salerno, jury Jean-Loup Amselle, Elio Grazioli, Rossella Salerno, Tobias Wendl, Paris, 27 juin 2011. CC by-sa
The Biennale de Dakar as a project of cooperation and development
The study observes the international art system from Dak’Art, the Senegalese contemporary African art biennale; in particular it explores the relationship between visual arts, spatial dynamics, cultural policies and the market; it is based on the keywords cooperation, development, territory and representation. The research analyses the international phenomena of biennial exhibitions, the ones in Africa, the history of the Dakar biennale, contemporary art and its landscape, contemporary African art historiography, the network of Dak’Art and the way contemporary productions are structured as “projects”. It appears clearly that culture is more and more often structured as “projects”; contemporary African art is a brand for the import-export of cultural goods; the network is the central resource of a cultural event and the wider and the more fragmented this network is, the more difficult it is to satisfy it; the geography of cultural events is defined by its international links; cultural events generate landscapes, a combination and interrelation of natural and human factors. The contemporary art system observed from the biennial art exhibition of Dakar appears strongly influenced by the funding organizations, and closely related to cultural policies and to the market, even though it doesn’t necessarily imply the selling of artworks within a gallery.
Bulimia nervosa is an eating disorder characterized by binge eating followed by purging. It is derived from Greek words meaning "ox" and "hunger" referring to the cycles of overeating and purging. Common causes include perfectionism, fear, guilt, and depression. Therapists use different approaches - some take a more authoritative role while others empower clients. Outreach programs aim to address the root causes of insecurity and perfectionism in teenagers to prevent eating disorders from developing.
The Moverio BT-200 is a binocular see-through smart glasses device that allows for augmented reality applications. It has a high resolution display, runs Android 4.0, and includes sensors, connectivity options, and a processor to enable hands-free augmented reality and virtual reality experiences. The document discusses how the Moverio BT-200 improves on previous smart glasses and creates new opportunities for developers to build augmented reality applications.
This document discusses different number systems including decimal, binary, octal, and hexadecimal. It explains how numbers are represented in each system using positional notation. Conversion between these number systems is demonstrated through examples. The document also covers signed integer representation methods like sign-and-magnitude, one's complement, and two's complement. Finally, it briefly introduces representation of characters using coding standards.
The document discusses digital systems and binary numbers. It defines digital systems as systems that manipulate discrete elements of information, such as binary digits represented by the values 0 and 1. It explains how binary numbers are represented and arithmetic operations like addition, subtraction, multiplication and division are performed on binary numbers. It also discusses number base conversions between decimal, binary, octal and hexadecimal numbering systems. Finally, it covers binary complements including 1's complement, 2's complement and subtraction using complements.
This document discusses various data representation systems used in computers, including:
- Binary, decimal, hexadecimal, and octal number systems. Binary uses two digits (0,1) while other systems use bases of 10, 16, and 8 respectively.
- Units of data representation such as bits, bytes, kilobytes, megabytes and gigabytes which are used to measure computer storage.
- Methods for converting between number systems, including dividing numbers into place values and multiplying digits by their place values.
- Special codes like Binary Coded Decimal (BCD) which represents each decimal digit with 4 binary bits.
- Binary arithmetic operations and how addition works the same in any number system by following
This document provides lecture notes on digital system design. It covers topics like logic simplification, combinational logic design, understanding binary and other number systems, binary operations, and Boolean algebra. The first section discusses decimal, binary, octal and hexadecimal number systems. Later sections explain binary addition, subtraction, multiplication and conversions between number bases. Signed number representations like 1's complement and 2's complement are also introduced. Finally, the document discusses Boolean algebra, logic functions, truth tables, and basic logic gates like AND and INVERTER.
The document discusses digital and analog systems. It explains that digital systems represent information as discrete values using bits, whereas analog systems represent information as continuous values. It provides examples of digital and analog signals and discusses how a continuous analog signal can be converted to a discrete digital signal through sampling and quantization. It also covers binary, octal, and hexadecimal number systems and how to convert between them. Finally, it discusses binary addition and subtraction using complement representations.
Numeral Systems: Positional and Non-Positional
Conversions between Positional Numeral Systems: Binary, Decimal and Hexadecimal
Representation of Numbers in Computer Memory
Exercises: Conversion between Different Numeral Systems
The document outlines key concepts in digital logic design and binary numbers, including:
- Digital systems represent information using discrete binary values of 0 and 1, unlike analog systems which use continuous values.
- Binary, octal, decimal, and hexadecimal number systems are examined, including how to convert between them.
- Binary addition, subtraction, multiplication and complements are explained through examples.
- 1's complement, 2's complement and radix complement operations are defined for binary numbers, allowing subtraction to be performed by addition of complements.
This document provides an overview of digital systems and binary numbers. It discusses topics such as analog vs digital signals, different number systems including binary, octal, decimal and hexadecimal, binary operations like addition and multiplication, and number base conversions. It also covers binary complements including 1's complement and 2's complement, which are important for signed binary numbers and binary subtraction.
This document provides an introduction to a digital design course. It discusses the recommended textbook, course description, grading breakdown, and course outline. The course focuses on fundamental digital concepts like number systems, Boolean algebra, logic gates, combinational and sequential logic. It will cover topics such as binary numbers, Boolean functions, logic gate minimization, adders/subtractors, multiplexers, flip-flops, and finite state machines. Students are expected to attend every lecture and participate in classroom discussions. Grades will be based on projects, midterm exams, and quizzes/assignments.
The document provides information about digital electronics and digital systems. It introduces digital logic and how digital systems represent information using discrete binary values of 0 and 1. Digital computers are able to manipulate this discrete digital data through programs. Common number systems like binary, octal, hexadecimal and their conversions to decimal are explained. Signed and unsigned binary numbers are also discussed.
Digital Logic Design Lecture 1A provides an overview of digital systems and binary numbers. It introduces the difference between analog and digital signals, the process of digitization, and the binary number system. The key concepts covered include representing numbers in binary format, converting between binary and decimal number systems using positional notation and weighted values, and introducing octal and hexadecimal numbering bases.
This document discusses number systems and Boolean algebra concepts relevant to switching theory and logic design. It covers topics like number systems, binary codes, Boolean algebra theorems and properties, switching functions, logic gate simplification, and multilevel logic implementations. Various number representations are examined, including binary, octal, hexadecimal, and binary coded decimal. Conversion between number bases is demonstrated. Boolean concepts like complements, addition, and subtraction using 1's and 2's complement are also summarized.
Inductive programming incorporates all approaches which are concerned with learning programs or algorithms from incomplete (formal) specifications. Possible inputs in an IP system are a set of training inputs and corresponding outputs or an output evaluation function, describing the desired behavior of the intended program, traces or action sequences which describe the process of calculating specific outputs, constraints for the program to be induced concerning its time efficiency or its complexity, various kinds of background knowledge such as standard data types, predefined functions to be used, program schemes or templates describing the data flow of the intended program, heuristics for guiding the search for a solution or other biases.
Output of an IP system is a program in some arbitrary programming language containing conditionals and loop or recursive control structures, or any other kind of Turing-complete representation language.
In many applications the output program must be correct with respect to the examples and partial specification, and this leads to the consideration of inductive programming as a special area inside automatic programming or program synthesis, usually opposed to 'deductive' program synthesis, where the specification is usually complete.
In other cases, inductive programming is seen as a more general area where any declarative programming or representation language can be used and we may even have some degree of error in the examples, as in general machine learning, the more specific area of structure mining or the area of symbolic artificial intelligence. A distinctive feature is the number of examples or partial specification needed. Typically, inductive programming techniques can learn from just a few examples.
The diversity of inductive programming usually comes from the applications and the languages that are used: apart from logic programming and functional programming, other programming paradigms and representation languages have been used or suggested in inductive programming, such as functional logic programming, constraint
programming, probabilistic programming
Research on the inductive synthesis of recursive functional programs started in the early 1970s and was brought onto firm theoretical foundations with the seminal THESIS system of Summers[6] and work of Biermann.[7] These approaches were split into two phases: first, input-output examples are transformed into non-recursive programs (traces) using a small set of basic operators; second, regularities in the traces are searched for and used to fold them into a recursive program. The main results until the mid 1980s are surveyed by Smith.[8] Due to
This document discusses how to convert between different number systems, including:
- Binary, decimal, octal, and hexadecimal.
- Rules for conversion include representing the place value of each digit and repeating division/multiplication.
- Examples are provided for converting between each system, such as binary to decimal, decimal to octal, and hexadecimal to binary.
- Octal and hexadecimal systems are useful because they provide a shorter representation of binary numbers and are less error prone than writing long binary numbers.
Number systems - Efficiency of number system, Decimal, Binary, Octal, Hexadecimalconversion
from one to another- Binary addition, subtraction, multiplication and division,
representation of signed numbers, addition and subtraction using 2’s complement and I’s
complement.
Binary codes - BCD code, Excess 3 code, Gray code, Alphanumeric code, Error detection
codes, Error correcting code.Deepak john,SJCET-Pala
Chapter 1 Digital Systems and Binary Numbers.pptAparnaDas827261
Digital Systems and Binary Numbers
- Digital systems manipulate discrete elements of information represented in binary form.
- The binary number system uses only two digits, 0 and 1, with place values that are powers of two.
- Conversions can be made between decimal, binary, octal, and hexadecimal number systems through arithmetic operations and grouping bits.
This document discusses different numeral systems including binary, decimal, and hexadecimal. It provides details on:
- How each system represents numbers using different bases and numerals
- Converting between the numeral systems by multiplying digits by their place value or dividing and taking remainders
- How computers internally represent integer and floating-point numbers, including sign representation and IEEE 754 standard
- How text is encoded using character codes like ASCII and stored as strings with null terminators
This document outlines the topics covered in the 21EC201 - Digital Principles and System Design course. It includes an introduction to number systems, logic gates, combinational logic circuits, Boolean algebra, truth tables and Karnaugh maps. Specific topics mentioned are binary, decimal, octal and hexadecimal number systems, logic gates like AND, OR, NAND, NOR, XOR and XNOR, arithmetic operations in binary and conversions between different number systems.
A typical CD player uses both analog and digital systems. It accepts digital data from the CD drive in the form of binary numbers like 10110011101. This digital data is then converted to an analog audio signal by a digital-to-analog converter. The analog audio signal is then amplified by a linear amplifier and output as sound waves by the speaker. This allows the CD player to take advantage of storing music digitally on the CD while outputting it in an analog format that can be heard.
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How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
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A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
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How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
2. 2.1 Decimal, Binary, Octal and Hexadecimal
Numbers
2.2 Relation between binary number system
with other number system
2.3 Representation of integer, character and
floating point numbers in binary
2.4 Binary Arithmetic
2.5 Arithmetic Operations for One’s
Complement, Two’s Complement, magnitude
and sign and floating point number
Ebooks.edhole.com
3. Most numbering system use positional
notation :
N = anrn + an-1rn-1 + … + a1r1 + a0r0
Where:
N: an integer with n+1 digits
r: base
ai {0, 1, 2, … , r-1}
Ebooks.edhole.com
4. Examples:
a) N = 278
r = 10 (base 10) => decimal numbers
symbol: 0, 1, 2, 3, 4, 5, 6,
7, 8, 9 (10 different symbols)
N = 278 => n = 2;
a2 = 2; a1 = 7; a0 = 8
278 = (2 x 102) + (7 x 101) + (8 x 100)
N = anrn + an-1rn-1 + … + a1r1 + a0r0
Ebooks.edhole.com
Hundreds Tens Ones
5. N = anrn + an-1rn-1 + … + a1r1 + a0r0
b) N = 10012
r = 2 (base-2) => binary numbers
symbol: 0, 1 (2 different symbols)
N = 10012 => n = 3;
a3 = 1; a2 = 0; a1 = 0; a0 = 1
10012 = (1 x 23)+(0 x 22)+(0 x 21)+(1 x 20)
c) N = 2638
r = 8 (base-8) => Octal numbers
symbol : 0, 1, 2, 3, 4, 5, 6, 7,
(8 different symbols)
N = 2638 => n = 2; a2 = 2; a1 = 6; a0 = 3
2638 = (2 x 82) + (6 x 81) + (3 x 80)
Ebooks.edhole.com
6. d) N = 26316
r = 16 (base-16) => Hexadecimal
numbers
symbol : 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, A, B, C, D, E, F
(16 different symbols)
N = 26316 => n = 2;
a2 = 2; a1 = 6; a0 = 3
26316 = (2 x 162)+(6 x 161)+(3 x 160)
Ebooks.edhole.com
7. Decimal Binary Octal Hexadecimal
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
16 10000 20 10
There are also non-positional numbering systems.
Example: Roman Number System
1987 = MCMLXXXVII
Ebooks.edhole.com
8. Binary and Decimal
◦ Converting a decimal number into binary
(decimal binary)
Divide the decimal number by 2 and take its
remainder
The process is repeated until it produces
the result of 0
The binary number is obtained by taking the
remainder from the bottom to the top
Ebooks.edhole.com
10. 0.8110 => 0.81 x 2 = 1.62
0.62 x 2 = 1.24
0.24 x 2 = 0.48
0.1100112
0.48 x 2 = 0.96
0.96 x 2 = 1.92
0.92 x 2 = 1.84
= 0.1100112 (approximately)
Ebooks.edhole.com
11. Converting a binary number into decimal
(binary decimal)
Multiply each bit in the binary number
with the weight (or position)
Add up all the results of the
multiplication performed
The desired decimal number is the
total of the multiplication results
performed
13. Theorem
If base R1 is the integer power of
other base, R2, i.e.
R1 = R2
d
e.g., 8 = 23
Every group of d digits in R2
(e.g., 3 digits)is equivalent to
1 digit in the R1 base
(Note: This theorem is used to convert
binary numbers to octal and hexadecimal
or the other way round)
Ebooks.edhole.com
14. From the theorem, assume that
R1 = 8 (base-8) octal
R2 = 2 (base-2) binary
From the theorem above,
d
R1 = R2
8 = 23
So, 3 digits in base-2 (binary) is
equivalent to 1 digit in base-8
(octal)
Ebooks.edhole.com
15. From the stated theorem, the
following is a binary-octal
conversion table.
Binary Octal
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7
In a computer
system, the
conversion from
binary to octal or
otherwise is based
on the conversion
table above.
3 digits in base-2 (binary) is equivalent to 1 digit in base-8 (octal)
16. Convert these binary numbers into octal
numbers:
(a) 001011112 (8 bits) (b) 111101002 (8 bits)
Refer to the binary-octal
conversion table
000 101 111
0 5 7
= 578
Refer to the binary-octal
conversion table
011 110 100
3 6 4
= 3648
Ebooks.edhole.com
17. Binary and Hexadecimal
• The same method employed in binary-octal
conversion is used once again.
• Assume that:
R1 = 16 (hexadecimal)
R2 = 2 (binary)
• From the theorem: 16 = 24
Hence, 4 digits in a binary number is
equivalent to 1 digit in the hexadecimal
number system (and otherwise)
• The following is the binary-hexadecimal
conversion table
Ebooks.edhole.com
18. Binary Hexadecimal
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
Example:
1. Convert the following
binary numbers into
hexadecimal numbers:
(a) 001011112
Refer to the binary-hexadecimal
conversion table
above
0010 11112 = 2F16
2 F
Ebooks.edhole.com
19. Convert the following octal numbers
into hexadecimal numbers (16 bits)
(a) 658 (b) 1238
Refer to the binary-octal conversion table
68 58
110 101
0000 0000 0011 01012
0 0 3 5
= 3516
Refer to the binary-octal conversion table
18 28 38
001 010 011
0000 0000 0101 00112
0 0 5 3
= 5316
octal binary hexadecimal
20. Convert the following hexadecimal
numbers into binary numbers
(a) 12B16 (b) ABCD16
Refer to the binary-hexadecimal
conversion table
1 2 B16
0001 0010 10112 (12 bits)
= 0001001010112
Refer to the binary-hexadecimal
conversion table
A B C D16
1010 1011 1101 11102
= 10101011110111102
25. Introduction
Machine instructions operate on data. The most
important general categories of data are:
1. Addresses – unsigned integer
2. Numbers – integer or fixed point, floating point
numbers and decimal (eg, BCD (Binary Coded Decimal))
3. Characters – IRA (International Reference
Alphabet), EBCDIC (Extended Binary Coded Decimal
Interchange Code), ASCII (American Standard Code for
Information Interchange)
4. Logical Data
- Those commonly used by computer users/programmers: signed
integer, floating point numbers and characters
26. Integer Representation
-1101.01012 = -13.312510
Computer storage & processing
do not have benefit of minus
signs (-) and periods.
Need to represent the integer
27. Signed Integer Representation
Signed integers are usually used
by programmers
Unsigned integers are used for
addressing purposes in the
computer (especially for
assembly language programmers)
Three representations of signed
integers:
1. Sign-and-Magnitude
2. Ones Complement
3. Twos Complement
28. The easiest representation
The leftmost bit in the binary number
represents the sign of the number. 0
if positive and 1 if negative
The balance bits represent the
magnitude of the number.
31. In the ones complement representation,
positive numbers are same as that of
sign-and-magnitude
Example: +5 = 00000101 (8 bit)
as in sign-and-magnitude representation
Sign-and-magnitude and ones complement
use the same representation above for +5
with 8 bits and all positive numbers.
For negative numbers, their
representation are obtained by changing
bit 0 → 1 and 1 → 0 from their positive
numbers
32. Convert –5 into ones complement
representation (8 bit)
Solution:
First, obtain +5 representation
in 8 bits 00000101
Change every bit in the number
from 0 to 1 and vice-versa.
–510 in ones complement is
111110102
33. Get the representation of ones
complement (6 bit) for the
following numbers:
i) +710 ii) –1010
Solution:
(+7) = 0001112
Solution:
(+10)
10
= 0010102
So,
(-10)
10
= 1101012
34. Similar to ones complement, its
positive number is same as sign-and-
magnitude
Representation of its negative
number is obtained by adding 1 to
the ones complement of the
number.
35. Convert –5 into twos complement
representation and give the
answer in 8 bits.
Solution:
First, obtain +5 representation in 8
bits 000001012
Obtain ones complement for –5
111110102
Add 1 to the ones complement number:
111110102 + 12 = 111110112
–5 in twos complement is 111110112
36. Obtain representation of twos
complement (6 bit) for the
following numbers
i) +710 ii)–1010
Solution:
(+7) = 0001112
(same as sign-magnitude)
Solution:
(+10)
10
= 0010102
(-10)
10
= 1101012 + 12
= 1101102
So, twos compliment
for –10 is 1101102
37. Obtain representation for the following
numbers
Decimal Sign-magnitude Twos complement
+7
+6
4 bits
-4
-6
-7
+18
-18
8 bits
-13
39. For character data type, its
representation uses codes such as the
ASCII, IRA or EBCDIC.
Note: Students are encouraged to
obtain the codes
40. In binary, floating point
numbers are represented in the
form of : +S x B+E and the number
can be stored in computer words
with 3 fields:
i) Sign (+ve, –ve)
ii) Significant S
iii) Exponent E
and B is base is implicit and
need not be stored because it is
the same for all numbers (base-
2).
45. Example:
i. 0101112 - 0011102 = 0010012
ii. 1000112 - 0111002 = 0001112
Exercise:
i. 1000100 – 010010
ii. 1010100 + 1100
iii. 110100 – 1001
iv. 11001 x 11
v. 110111 + 001101
vi. 111000 + 1100110
vii. 110100 x 10
viii. 11001 - 1110
46. Addition and subtraction for
signed integers
Reminder: All subtraction
operations will be changed into
addition operations
Example: 8 – 5 = 8 + (–5)
–10 + 2 = (–10) + 2
6 – (–3) = 6 + 3
47. Z = X + Y
There are a few possibilities:
i. If both numbers, X and Y are
positive
o Just perform the addition operation
Example:
510 + 310 = 0001012 + 0000112
= 0010002
= 810
48. ii. If both numbers are negative
o Add |X| and |Y| and set the sign bit = 1
to the result, Z
Example: –310 – 410 = (–3) + (–4)
= 1000112 + 1001002
Only add the magnitude, i.e.:
000112 + 001002 = 001112
Set the sign bit of the result
(Z) to 1 (–ve)
= 1001112
= –710
49. iii. If signs of both number differ
o There will be 2 cases:
a) | +ve Number | > | –ve Number |
Example: (–2) + (+4), (+5) + (–3)
◦ Set the sign bit of the –ve
number to 0 (+ve), so that both
numbers become +ve.
◦ Subtract the number of smaller
magnitude from the number with a
bigger magnitude
50. Sample solution:
Change the sign bit of the –ve number to
+ve
(–2) + (+4) = 1000102 + 0001002
= 0001002 – 0000102
= 0000102 = 210
b) | –ve Number | > | +ve Number |
◦ Subtract the +ve number from the –ve number
Example: (+310) + (–510)
= 0000112 + 1001012
= 1001012 – 0000112
= 1000102
= –210
51. In ones complement, it is easier than sign-and-
magnitude
Change the numbers to its representation
and perform the addition operation
However a situation called Overflow might
occur when addition is performed on the
following categories:
1. If both are negative numbers
2. If both are in difference sign and
|+ve Number| > | –ve Number|
52. Overflow => the addition result
exceeds the number of bits that was
fixed
1. Both are –ve numbers
Example: –310 – 410 = (–310) + (–410)
Solution:
◦Convert –310 and –410 into ones
complement representation
+310 = 000000112 (8 bits)
–310 = 111111002
+410 = 000001002 (8 bits)
–410 = 111110112
53. • Perform the addition operation
(–310) => 11111100 (8 bit)
+(–410) => 11111011 (8 bit)
–710 111110111 (9 bit)
Overflow occurs. This value is called EAC and needs to be
added to the rightmost bit.
11110111
+ 1
111110002 = –710
the answer
54. 2. | +ve Number| > |–ve Number|
• This case will also cause an
overflow
Example: (–2) + 4 = (–2) + (+4)
Solution:
• Change both of the numbers above
into one’s complement
representation
–2 = 111111012 +4 = 000001002
• Add both of the numbers
(–210) => 11111101 (8 bit)
+ (+410) => 00000100 (8 bit)
+210 100000001 (9 bit)
There is an EAC
55. • Add the EAC to the rightmost bit
00000001
+ 1
000000102 = +210
the answer
Note:
For cases other than 1 & 2 above, overflow does not occur
and there will be no EAC and the need to perform addition to
the rightmost bit does not arise
56. Addition operation in twos
complement is same with that of
ones complement, i.e. overflow
occurs if:
1. If both are negative numbers
2. If both are in difference and
|+ve Number| > |–ve Number|
58. Perform addition operation on
both the numbers in twos
complement representation and
ignore the EAC.
111100 (–310)
111011 (–410)
1111001
Ignore the
EAC
The answer
= 1110012 (two’s complement)
= –710
59. Note:
In two’s complement, EAC is
ignored (do not need to be added
to the leftmost bit, like that of
one’s complement)
60. Example: (–2) + 4 = (–2) + (+4)
Solution:
Change both of the numbers above
into twos complement representation
–2 = 1111102 +4 = 0001002
Perform addition operation on both
numbers
(–210) => 111110 (6 bit)
+ (+410) => 000100 (6 bit)
+210 1000010
Ignore the EAC
61. The answer is 0000102 = +210
Note: For cases other than 1 and 2
above, overflow does not occur.
Exercise:
Perform the following arithmetic
operations in ones complement and also
twos complement
1. (+2) + (+3) [6 bit]
2. (–2) + (–3) [6 bit]
3. (–2) + (+3) [6 bit]
4. (+2) + (–3) [6 bit]
Compare your answers with the stated
theory