The document describes Vladimir Cuesta's proposed Cuesta Computer, which uses a binary arithmetic software and hardware based on bits. Numbers and symbols are represented uniquely in binary using a convention of empty spaces. Examples show entering combinations of numbers and symbols and obtaining the corresponding words, phrases, or calculations based on the binary representations. The computer aims to efficiently use available space by employing bits as basic units rather than bytes.
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.
This document provides an overview of a logic design course, including its objectives, topics, and schedule. The course aims to give students an understanding of binary systems, Boolean algebra, logic gates, combinational and sequential circuits. Key topics include number systems, Boolean logic, minimization techniques, logic gates, arithmetic circuits, flip-flops, counters, and memory devices. The course is scheduled over 16 weeks, with topics like number systems in the first few weeks and sequential circuits in the later weeks.
This document provides an overview of digital logic circuits. It begins with an introduction to logic gates and Boolean algebra. Common logic gates like AND, OR, NOT are described along with their truth tables. Boolean algebra is discussed as a way to analyze and synthesize digital logic circuits using Boolean variables and logic operations. Combinational logic and sequential logic are defined. Techniques for simplifying Boolean functions are covered, including Karnaugh maps and Boolean identities. Implementation of logic functions using sum-of-products form is also summarized.
This document contains problems related to Boolean algebra and logic gates. It asks the reader to:
- Convert between binary, decimal, hexadecimal, and octal number systems
- Derive truth tables for logic gates and Boolean functions
- Use Boolean algebra to simplify and prove equivalences between Boolean functions
- Express Boolean functions in sum of products and product of sums form
- Write Boolean functions in canonical form using minterms and maxterms
This document provides an overview of digital logic circuits. It begins with an introduction to logic gates and Boolean algebra. Common logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR are explained along with their truth tables. Boolean algebra identities and theorems like De Morgan's theorem are discussed. Karnaugh maps are introduced as a method for simplifying Boolean functions. The document also covers combinational logic, sequential logic, implementation of logic functions using sum-of-products form and provides examples of logic circuit design.
The document discusses several greedy algorithm problems:
1. The knapsack problem which involves filling a knapsack with objects to maximize total value while not exceeding weight capacity. Objects are sorted by value/weight ratio.
2. The chemistry reagents problem which involves storing reagents in refrigerators where each refrigerator has a set temperature. The minimum number of refrigerators is determined.
3. The overlapping circles problem which counts the maximum number of exterior circles on an x-axis where each circle is defined by its center and radius. Intervals are sorted and a maximum number of disjoint intervals is found.
This document discusses greedy algorithms and divide and conquer algorithms. It provides examples of problems that can be solved using each approach and outlines the general solutions. For greedy algorithms, it explains that they make locally optimal choices at each step without considering future possibilities. For divide and conquer, it explains the three main steps of dividing the problem into subproblems, solving the subproblems recursively, and merging the solutions. It also provides an example problem of finding the number of inversions in an array by modifying the merge sort algorithm.
Introduction to Information Technology Lecture 2MikeCrea
Number Systems
Types of number systems
Number bases
Range of possible numbers
Conversion between number bases
Common powers
Arithmetic in different number bases
Shifting a number
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.
This document provides an overview of a logic design course, including its objectives, topics, and schedule. The course aims to give students an understanding of binary systems, Boolean algebra, logic gates, combinational and sequential circuits. Key topics include number systems, Boolean logic, minimization techniques, logic gates, arithmetic circuits, flip-flops, counters, and memory devices. The course is scheduled over 16 weeks, with topics like number systems in the first few weeks and sequential circuits in the later weeks.
This document provides an overview of digital logic circuits. It begins with an introduction to logic gates and Boolean algebra. Common logic gates like AND, OR, NOT are described along with their truth tables. Boolean algebra is discussed as a way to analyze and synthesize digital logic circuits using Boolean variables and logic operations. Combinational logic and sequential logic are defined. Techniques for simplifying Boolean functions are covered, including Karnaugh maps and Boolean identities. Implementation of logic functions using sum-of-products form is also summarized.
This document contains problems related to Boolean algebra and logic gates. It asks the reader to:
- Convert between binary, decimal, hexadecimal, and octal number systems
- Derive truth tables for logic gates and Boolean functions
- Use Boolean algebra to simplify and prove equivalences between Boolean functions
- Express Boolean functions in sum of products and product of sums form
- Write Boolean functions in canonical form using minterms and maxterms
This document provides an overview of digital logic circuits. It begins with an introduction to logic gates and Boolean algebra. Common logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR are explained along with their truth tables. Boolean algebra identities and theorems like De Morgan's theorem are discussed. Karnaugh maps are introduced as a method for simplifying Boolean functions. The document also covers combinational logic, sequential logic, implementation of logic functions using sum-of-products form and provides examples of logic circuit design.
The document discusses several greedy algorithm problems:
1. The knapsack problem which involves filling a knapsack with objects to maximize total value while not exceeding weight capacity. Objects are sorted by value/weight ratio.
2. The chemistry reagents problem which involves storing reagents in refrigerators where each refrigerator has a set temperature. The minimum number of refrigerators is determined.
3. The overlapping circles problem which counts the maximum number of exterior circles on an x-axis where each circle is defined by its center and radius. Intervals are sorted and a maximum number of disjoint intervals is found.
This document discusses greedy algorithms and divide and conquer algorithms. It provides examples of problems that can be solved using each approach and outlines the general solutions. For greedy algorithms, it explains that they make locally optimal choices at each step without considering future possibilities. For divide and conquer, it explains the three main steps of dividing the problem into subproblems, solving the subproblems recursively, and merging the solutions. It also provides an example problem of finding the number of inversions in an array by modifying the merge sort algorithm.
Introduction to Information Technology Lecture 2MikeCrea
Number Systems
Types of number systems
Number bases
Range of possible numbers
Conversion between number bases
Common powers
Arithmetic in different number bases
Shifting a number
Iron Road is developing the Central Eyre Iron Project (CEIP) in South Australia. CEIP is a large magnetite project that has completed a pre-feasibility study examining a potential 10Mtpa operation. Drilling has defined a mineral resource of 1.2 billion tonnes at CEIP so far. Infrastructure and community studies are underway to support developing the project.
Zimtu Capital Corp. has completed an initial field program on rare earth element projects in British Columbia through partnerships with private companies. The program included prospecting, sampling and analysis of properties located along the Rocky Mountain Rare Metal Belt, a region known to contain rare earth and rare metal deposits. Preliminary samples returned anomalous indicator elements. Zimtu will assess results to identify partners to advance properties and is also sponsoring a University of British Columbia study on the mineralization of the belt.
Historical report by the British Columbia Geological Survey on carbonatites and related rocks. Ther report was completed by geologist Jennifer Pell who has spent several years studying rare metals in British Columbia's Rocky Mountain Rare Metal Belt.
London Mining is moving towards exploiting its Isua iron ore project in Greenland. It completed a feasibility study and environmental assessments in 2011. Construction is scheduled to start in 2012 to develop the mine and infrastructure, with production planned to begin in 2015.
True North Gems is preparing its Aappaluttoq ruby and pink sapphire project for a mining permit. It has explored the site since 2004 through drilling and sampling. It is conducting feasibility studies and environmental assessments to submit for exploitation approval.
TANBREEZ Mining Greenland is undertaking metallurgical testing and feasibility studies for its zirconium-rare earth deposit to establish processing parameters for exploitation. Test results show the valuable minerals
1) Greenland has potential for rare earth element deposits related to various geological settings like carbonatite magmatism and alkaline intrusions.
2) A workshop was conducted by GEUS and BMP to assess Greenland's rare earth element potential and provide data to the exploration industry.
3) The workshop evaluated 35 areas in Greenland and identified known rare earth element deposits as well as geological environments favorable for hosting undiscovered deposits.
Invest in Rare Earth Metals - Terra Metal Fund LVG AG
Invest in Strategic and Rare Earth Metals via Terra Metal Fund
http://www.mylifeplan.info/
Investments in tangible values offer extensive protection against inflation. Limited supplies and consistent advances in technology (smartphones, iPads, flat screen monitors etc.) around the world create continuously growing demand for strategic and rare earth metals - even during cyclically weaker periods of global economic growth.
A great introduction to the Rare Earths Elements.
International Montoro Resources Inc. wishes to clarify statements made by Boss Power Corp. regarding a settlement between Boss Power and the Province of British Columbia. Specifically, Montoro states that its IMT-Cup Lake claims adjoining the Blizzard properties are not part of the settlement. Montoro plans to proceed with its own claim against the Province of B.C. seeking compensation for the expropriation of its Cup Lake/Donen properties east of Kelowna. Montoro holds interests in properties prospective for rare earth elements and uranium in British Columbia and Saskatchewan.
Montoro Resources Inc. has acquired additional mineral claims in its Tacheeda Lake claim block northeast of Prince George, BC. The claims cover an area of 1,065.10 hectares and adjoin a previously developed limestone quarry. Montoro plans to develop this quarry and secure permits. The acquisition allows Montoro to continue developing targets identified in a recent airborne geophysical survey. Terms of the acquisition include cash, shares, and warrants paid to the vendor as well as a 1% net smelter royalty. The claims increase Montoro's land holdings in the area to 24 tenures covering 8,650 hectares prospective for rare earth elements.
Behind the Performance of Quake 3 Engine: Fast Inverse Square RootMaksym Zavershynskyi
Quake 3 was probably the most famous first-person shooter back in 1999. It had fascinating graphics and very high-responsiveness which is the result of a performance optimization and high-quality code written by id
Software team. One of the most famous optimization tricks is the function that computes the approximate of inverse (reciprocal) square root through some clever bit hacking. This function is the subject of investigations by mathematicians and programmers even today. In this presentation we try to understand how it works and we also try to find the author.
Digital logic design deals with digital circuits and how to design digital hardware using logic gates. It involves working with binary and other number systems. Binary represents information using two states (0 and 1) which can be represented electrically using voltage levels. Converting between number systems like binary, decimal, and octal allows digital components to interface. Basic logic operations like addition, subtraction and multiplication can then be performed on binary numbers.
This document contains an exercise on digital electronics concepts including:
1. The differences between analog and digital measurements and pros and cons of analog vs digital electronics.
2. Tables defining binary, octal, decimal, and hexadecimal number systems.
3. Practice problems converting between number systems and performing basic binary math operations like addition, subtraction, multiplication, and division.
4. An independent practice section with additional problems converting between number systems and performing binary math.
This presentation will help you with the current status of numbers, their conversions and things which it governs on and things which is totally dependent on numbers like our personal computers, etc.
This document provides an overview of topics related to algorithms, pseudo code, binary number systems, and Morse code. It includes objectives, examples, and activities for each topic. Students will learn about defining pseudo code, writing algorithms, binary number representation, addition and subtraction in binary, and Morse code encryption/decryption. Practice problems are provided to convert between binary and decimal numbers, perform binary operations, and write pseudo code.
The document discusses number systems and data representation in computers. It explains that computers use the binary number system to represent numeric and alphanumeric data. Binary representations allow computers to distinguish different states using digits of 0 and 1. The key points are:
- Computers use the binary system to represent data as strings of bits (0s and 1s) that can be processed electronically
- Numeric data such as integers are represented using binary formats like binary, sign-magnitude, 1's complement, and 2's complement
- Text and character data are represented using coding schemes like ASCII which assign a unique binary code to each character
- Floating point representation is used to store real numbers in a binary format using a sign bit,
The document discusses digital logic circuits and their components. It begins with an introduction to logic gates, which are the basic building blocks of digital circuits. Common logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR are described along with their truth tables. Boolean algebra is then introduced as the mathematical system used to analyze and design digital logic circuits. Important concepts in boolean algebra like boolean functions, identities and logic simplification are covered. The document concludes by describing Karnaugh maps, a graphical technique used to simplify boolean functions into their minimum logic gate implementations.
This document provides an introduction and collection of problems related to bitwise operations and string manipulations. It begins with an introduction to bits, boolean functions, truth tables, and common bitwise operations like AND, OR, XOR, and shifts. The bulk of the document consists of 27 problems testing various concepts in bitwise logic and manipulations, such as simplifying boolean expressions, solving bitwise equations, and implementing logic gates using NAND gates. Solutions to the problems are not provided.
A basic understanding of computers, their functions, and their role in modern society. It involves knowing about computer hardware, software, and their applications.
1. The document presents a model for computing and evolution using monoids and binary arithmetic.
2. Two monoids are defined: ({0,1},+) representing binary addition, and ({0,1},.) representing binary multiplication.
3. Generations of ancestors are modeled backwards in time using binary operations and diagrams of 0s and 1s to represent family trees.
Monoids, Computer Science And Evolutionguest9fa195
1. The document presents a model for computing as two monoids - ({0,1},+) representing binary addition and ({0,1},.) representing binary multiplication.
2. It then extends this model to represent genealogical trees and reverse evolution by numbering generations with 0s and 1s using the same monoids.
3. Diagrams are shown representing multiple generations according to this model, with the first generation at the top moving backwards in time.
Binary code represents all data and instructions inside a computer using only the digits 0 and 1. It works by using place values that double in value at each place, from right to left, similar to our decimal system which uses place values that are 10 times greater at each place. Bytes, which are made up of 8 bits, can represent a single character by assigning a unique 8-bit binary number to each letter, number, and symbol. Understanding binary code is essential for learning computer programming and how computers work at a fundamental level.
Scaling IoT: Telemetry, Command & Control, Analytics and the CloudNick Landry
The document discusses the history and future of connectivity and computing from Henry IV's goal of a chicken in every pot to Bill Gates' vision of a computer on every desk. It then discusses how Moore's Law, Metcalf's Law, and Koomey's Law have driven exponential growth in transistors, connectivity, and computational power over time. The rest of the document discusses concepts like the Internet of Things (IoT), how IoT solutions work from initial device and data collection through data analytics and insights. It provides examples of how IoT could be used and concludes with resources for getting started with IoT.
The document discusses number representation in computers. It begins by introducing different number systems like decimal, binary, and hexadecimal. It then discusses how numeric data is stored in memory, including how integers, floats, characters and strings are represented. It also covers binary operations like addition, subtraction, multiplication and division. Finally, it discusses signed number representation using sign-magnitude, one's complement and two's complement methods.
Iron Road is developing the Central Eyre Iron Project (CEIP) in South Australia. CEIP is a large magnetite project that has completed a pre-feasibility study examining a potential 10Mtpa operation. Drilling has defined a mineral resource of 1.2 billion tonnes at CEIP so far. Infrastructure and community studies are underway to support developing the project.
Zimtu Capital Corp. has completed an initial field program on rare earth element projects in British Columbia through partnerships with private companies. The program included prospecting, sampling and analysis of properties located along the Rocky Mountain Rare Metal Belt, a region known to contain rare earth and rare metal deposits. Preliminary samples returned anomalous indicator elements. Zimtu will assess results to identify partners to advance properties and is also sponsoring a University of British Columbia study on the mineralization of the belt.
Historical report by the British Columbia Geological Survey on carbonatites and related rocks. Ther report was completed by geologist Jennifer Pell who has spent several years studying rare metals in British Columbia's Rocky Mountain Rare Metal Belt.
London Mining is moving towards exploiting its Isua iron ore project in Greenland. It completed a feasibility study and environmental assessments in 2011. Construction is scheduled to start in 2012 to develop the mine and infrastructure, with production planned to begin in 2015.
True North Gems is preparing its Aappaluttoq ruby and pink sapphire project for a mining permit. It has explored the site since 2004 through drilling and sampling. It is conducting feasibility studies and environmental assessments to submit for exploitation approval.
TANBREEZ Mining Greenland is undertaking metallurgical testing and feasibility studies for its zirconium-rare earth deposit to establish processing parameters for exploitation. Test results show the valuable minerals
1) Greenland has potential for rare earth element deposits related to various geological settings like carbonatite magmatism and alkaline intrusions.
2) A workshop was conducted by GEUS and BMP to assess Greenland's rare earth element potential and provide data to the exploration industry.
3) The workshop evaluated 35 areas in Greenland and identified known rare earth element deposits as well as geological environments favorable for hosting undiscovered deposits.
Invest in Rare Earth Metals - Terra Metal Fund LVG AG
Invest in Strategic and Rare Earth Metals via Terra Metal Fund
http://www.mylifeplan.info/
Investments in tangible values offer extensive protection against inflation. Limited supplies and consistent advances in technology (smartphones, iPads, flat screen monitors etc.) around the world create continuously growing demand for strategic and rare earth metals - even during cyclically weaker periods of global economic growth.
A great introduction to the Rare Earths Elements.
International Montoro Resources Inc. wishes to clarify statements made by Boss Power Corp. regarding a settlement between Boss Power and the Province of British Columbia. Specifically, Montoro states that its IMT-Cup Lake claims adjoining the Blizzard properties are not part of the settlement. Montoro plans to proceed with its own claim against the Province of B.C. seeking compensation for the expropriation of its Cup Lake/Donen properties east of Kelowna. Montoro holds interests in properties prospective for rare earth elements and uranium in British Columbia and Saskatchewan.
Montoro Resources Inc. has acquired additional mineral claims in its Tacheeda Lake claim block northeast of Prince George, BC. The claims cover an area of 1,065.10 hectares and adjoin a previously developed limestone quarry. Montoro plans to develop this quarry and secure permits. The acquisition allows Montoro to continue developing targets identified in a recent airborne geophysical survey. Terms of the acquisition include cash, shares, and warrants paid to the vendor as well as a 1% net smelter royalty. The claims increase Montoro's land holdings in the area to 24 tenures covering 8,650 hectares prospective for rare earth elements.
Behind the Performance of Quake 3 Engine: Fast Inverse Square RootMaksym Zavershynskyi
Quake 3 was probably the most famous first-person shooter back in 1999. It had fascinating graphics and very high-responsiveness which is the result of a performance optimization and high-quality code written by id
Software team. One of the most famous optimization tricks is the function that computes the approximate of inverse (reciprocal) square root through some clever bit hacking. This function is the subject of investigations by mathematicians and programmers even today. In this presentation we try to understand how it works and we also try to find the author.
Digital logic design deals with digital circuits and how to design digital hardware using logic gates. It involves working with binary and other number systems. Binary represents information using two states (0 and 1) which can be represented electrically using voltage levels. Converting between number systems like binary, decimal, and octal allows digital components to interface. Basic logic operations like addition, subtraction and multiplication can then be performed on binary numbers.
This document contains an exercise on digital electronics concepts including:
1. The differences between analog and digital measurements and pros and cons of analog vs digital electronics.
2. Tables defining binary, octal, decimal, and hexadecimal number systems.
3. Practice problems converting between number systems and performing basic binary math operations like addition, subtraction, multiplication, and division.
4. An independent practice section with additional problems converting between number systems and performing binary math.
This presentation will help you with the current status of numbers, their conversions and things which it governs on and things which is totally dependent on numbers like our personal computers, etc.
This document provides an overview of topics related to algorithms, pseudo code, binary number systems, and Morse code. It includes objectives, examples, and activities for each topic. Students will learn about defining pseudo code, writing algorithms, binary number representation, addition and subtraction in binary, and Morse code encryption/decryption. Practice problems are provided to convert between binary and decimal numbers, perform binary operations, and write pseudo code.
The document discusses number systems and data representation in computers. It explains that computers use the binary number system to represent numeric and alphanumeric data. Binary representations allow computers to distinguish different states using digits of 0 and 1. The key points are:
- Computers use the binary system to represent data as strings of bits (0s and 1s) that can be processed electronically
- Numeric data such as integers are represented using binary formats like binary, sign-magnitude, 1's complement, and 2's complement
- Text and character data are represented using coding schemes like ASCII which assign a unique binary code to each character
- Floating point representation is used to store real numbers in a binary format using a sign bit,
The document discusses digital logic circuits and their components. It begins with an introduction to logic gates, which are the basic building blocks of digital circuits. Common logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR are described along with their truth tables. Boolean algebra is then introduced as the mathematical system used to analyze and design digital logic circuits. Important concepts in boolean algebra like boolean functions, identities and logic simplification are covered. The document concludes by describing Karnaugh maps, a graphical technique used to simplify boolean functions into their minimum logic gate implementations.
This document provides an introduction and collection of problems related to bitwise operations and string manipulations. It begins with an introduction to bits, boolean functions, truth tables, and common bitwise operations like AND, OR, XOR, and shifts. The bulk of the document consists of 27 problems testing various concepts in bitwise logic and manipulations, such as simplifying boolean expressions, solving bitwise equations, and implementing logic gates using NAND gates. Solutions to the problems are not provided.
A basic understanding of computers, their functions, and their role in modern society. It involves knowing about computer hardware, software, and their applications.
1. The document presents a model for computing and evolution using monoids and binary arithmetic.
2. Two monoids are defined: ({0,1},+) representing binary addition, and ({0,1},.) representing binary multiplication.
3. Generations of ancestors are modeled backwards in time using binary operations and diagrams of 0s and 1s to represent family trees.
Monoids, Computer Science And Evolutionguest9fa195
1. The document presents a model for computing as two monoids - ({0,1},+) representing binary addition and ({0,1},.) representing binary multiplication.
2. It then extends this model to represent genealogical trees and reverse evolution by numbering generations with 0s and 1s using the same monoids.
3. Diagrams are shown representing multiple generations according to this model, with the first generation at the top moving backwards in time.
Binary code represents all data and instructions inside a computer using only the digits 0 and 1. It works by using place values that double in value at each place, from right to left, similar to our decimal system which uses place values that are 10 times greater at each place. Bytes, which are made up of 8 bits, can represent a single character by assigning a unique 8-bit binary number to each letter, number, and symbol. Understanding binary code is essential for learning computer programming and how computers work at a fundamental level.
Scaling IoT: Telemetry, Command & Control, Analytics and the CloudNick Landry
The document discusses the history and future of connectivity and computing from Henry IV's goal of a chicken in every pot to Bill Gates' vision of a computer on every desk. It then discusses how Moore's Law, Metcalf's Law, and Koomey's Law have driven exponential growth in transistors, connectivity, and computational power over time. The rest of the document discusses concepts like the Internet of Things (IoT), how IoT solutions work from initial device and data collection through data analytics and insights. It provides examples of how IoT could be used and concludes with resources for getting started with IoT.
The document discusses number representation in computers. It begins by introducing different number systems like decimal, binary, and hexadecimal. It then discusses how numeric data is stored in memory, including how integers, floats, characters and strings are represented. It also covers binary operations like addition, subtraction, multiplication and division. Finally, it discusses signed number representation using sign-magnitude, one's complement and two's complement methods.
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.
The document provides information about Boolean algebra over 3 paragraphs. It begins with an introduction to Boolean algebra and switching algebra, noting it uses binary logic (1 and 0) to perform mathematical operations. The second paragraph discusses basic logic functions like inverters, OR, and AND gates. The third paragraph explains that Boolean expressions can be implemented as logic circuits, providing an example circuit. The document summarizes key concepts in Boolean algebra in 3 sentences or less.
This document discusses the Luhn algorithm, which is used to validate identification numbers like credit card numbers. It describes the algorithm's strengths and weaknesses, provides an informal explanation of how it works with an example, and includes implementations in C# and pseudocode. The document also discusses how the Luhn algorithm is used to validate credit card numbers specifically, including the typical anatomy of a credit card number and how the check digit is generated.
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 document provides an overview of combinatorics and number theory concepts including basic counting techniques, recurrence relations, binomial coefficients, prime numbers, congruences, and proofs by induction. It discusses topics such as permutations, subsets, Pascal's triangle for calculating binomial coefficients efficiently, and using recurrence relations to solve problems like calculating the Fibonacci sequence or the number of ways to reach the last stage in a multi-stage process.
This document provides an overview of computer systems and programming. It defines a computer as a device that takes in raw data, processes it under a set of instructions called a program, and provides an output. Computers provide benefits like speed, accuracy, and ability to handle large workloads. The document then discusses computer hardware components, software components like operating systems and applications, and data representation in computers using bits, integers, and number systems. It also covers basic concepts in C++ programming like what a computer program is, compilers vs interpreters, and binary operations like addition and subtraction.
Similar to Cuesta Computer With Software Based On Binary Arithmetic And A Hardware Based On Bites I (20)
Gauge systems and functions, hermitian operators and clocks as conjugate func...vcuesta
This document summarizes a research article about gauge systems and constraints in physics. It discusses two key problems that can arise: 1) Clocks may not be well-defined over the entire phase space. 2) Quantum operators associated with complete observables may not be self-adjoint. The summary proposes selecting clocks such that their Poisson brackets with constraints are equal to 1. This is shown to solve the two problems for several example systems, including a free particle and a system with two constraints. Clocks and complete observables are constructed for the examples, and it is verified that the operators are self-adjoint.
Poster Gauge systems and functions, hermitian operators and clocks as conjuga...vcuesta
This document discusses gauge systems with constraints and complete observables at the quantum level. It examines two cases: a non-relativistic free particle with one constraint and a model with two constraints. For the particle, choosing a clock such that its Poisson bracket with the constraint is one solves problems of the clock not being defined at all times and the operator for a complete observable not being self-adjoint. For the two constraint model, choosing clocks conjugate to the constraints results in self-adjoint operators. The self-adjointness of operators for complete observables in more complex systems like field theory and general relativity requires further study.
Generalizations For Cartans Equations And Bianchi Identities For Arbitrary Di...vcuesta
This document presents generalizations of Cartan's structure equations and Bianchi identities for arbitrary dimensions. Actions are constructed for the generalized equations. Specifically:
1) Actions are constructed for 2D, 3D and nD involving the tetrad, connection, torsion, curvature and auxiliary fields.
2) Varying the actions yields generalized equations of motion that contain Cartan's equations and Bianchi identities as particular cases.
3) The generalized equations are sets of equations for 2-forms and 3-forms involving exterior derivatives and wedge products of the variables, similar to the original Cartan and Bianchi equations.
Realizations, Differential Equations, Canonical Quantum Commutators And Infin...vcuesta
1) The document discusses finding different realizations of quantum operators q and p that obey the canonical commutator [q,p]=iħ. It considers cases where p is defined as -iħf(q)∂/∂q and solves for the corresponding q operator.
2) This leads to an infinite number of possible representations, as f(q) can be any function of q. Three specific cases are analyzed.
3) For each case, the Schrodinger equation is derived and solutions are found for a free particle and infinite square well potential. However, some cases cannot yield normalizable wavefunctions or satisfy boundary conditions.
A Chronological Response Of The Immune Systemvcuesta
The document presents a model of the chronological response of the human immune system to an infectious process. The model includes the following components: T lymphocytes which coordinate the immune response; B lymphocytes which produce antibodies; granulocytes which mark infected cells; and monocytes which eliminate dead cells and genetic material. According to the model, when injury occurs granulocytes first mark infected cells, then T lymphocytes coordinate antibody production by B lymphocytes to fight the infection, and finally monocytes eliminate dead materials. The author proposes this model to explain the functions of these immune system components together in response to infection.
The hairy ball theorem states that it is impossible to define a non-vanishing tangent vector field of continuous directions on the surface of a sphere. While it is possible to define tangent vectors at individual points or finite sets of points on a sphere, it is not possible to consistently define tangent vectors at every point on the sphere simultaneously. The theorem generalizes to other closed surfaces in higher dimensions as well.
Quantum Transitions And Its Evolution For Systems With Canonical And Noncanon...vcuesta
1. The document studies the quantum transitions and time evolution of the phase space coordinates for the one-dimensional harmonic oscillator with both canonical and noncanonical symplectic structures.
2. For the canonical case, the solutions to the classical equations of motion and the quantum transitions between energy levels are obtained. The time evolution of the transition amplitudes between states is also determined.
3. An analogous analysis is performed for the noncanonical case, where modified commutation relations and modified expressions for the creation/annihilation operators are obtained. The quantum transitions and their time evolution are determined.
Conformal Anisotropic Mechanics And The HořAva Dispersion Relationvcuesta
This document summarizes a paper that implements scale anisotropic transformations between space and time in classical mechanics. This results in a system consistent with the dispersion relation proposed in Horava gravity. The paper constructs an action principle for a particle that is invariant under anisotropic scaling transformations between space and time. This action reduces to known systems like conformal mechanics in certain limits of the dynamical exponent z. The paper also analyzes the canonical formalism, equations of motion, symmetries and thermodynamic properties of this anisotropic mechanical system.
Proceedings A Method For Finding Complete Observables In Classical Mechanicsvcuesta
1. The document presents a new method for finding complete observables in classical mechanics, which are gauge invariant quantities.
2. The method starts with partial observables and clocks, which are non-gauge invariant phase space functions. Using constants of motion, the partial observables can be written in terms of the clocks to obtain complete observables.
3. As an example, the method is applied to a particle in a gravitational field, where the Hamiltonian is used as a constant of motion to write the position variable as a function of the momentum and time.
This document discusses Lie algebras and the Killing form. It defines Lie algebras and introduces the Killing form, showing that it is a contravariant tensor. It then explains that the signature of the diagonalized Killing form is an invariant that can be used to classify and identify isomorphic Lie algebras. Examples are provided of low-dimensional Lie algebras classified according to their Killing form signatures.
Different Quantum Spectra For The Same Classical Systemvcuesta
The document discusses how the one-dimensional and two-dimensional isotropic harmonic oscillators, which correspond to a single classical system each, can have multiple quantum spectra.
Specifically, it shows that:
1) The one-dimensional oscillator admits two different quantum spectra, obtained by defining creation/annihilation operators in two different ways.
2) Similarly, the two-dimensional oscillator is shown to have four distinct quantum spectra, as the x and y directions can be quantized independently using two different operator definitions each.
3) This demonstrates that the same classical system can lead to multiple quantum descriptions and spectra, contrary to some previous works that obtained a unique spectrum for different classical formulations.
Propositional Logic, Boolean Arithmetic And Binary Arithmeticvcuesta
1. The document discusses the relationships between propositional logic, Boolean algebra, and binary arithmetic.
2. It presents logic tables to express logical connectives like negation, conjunction, disjunction using only negation and conjunction. Similarly, it constructs tables using set operations and binary operations on 0s and 1s.
3. The goal is to show that logical operations can be expressed in terms of more basic ones, and that propositional logic relates to other branches of mathematics like sets and binary arithmetic.
Generation Of Solutions Of The Einstein Equations By Means Of The Kaluza Klei...vcuesta
1) The paper describes a method for generating new solutions to the Einstein-Maxwell equations coupled to a scalar field using the Kaluza-Klein formulation.
2) Starting from a solution that has a Killing vector field, one can obtain a one-parameter family of new solutions by decomposing the metric in different ways using different Killing vector fields.
3) As an example, the paper generates a new stationary, spherically symmetric solution from the Schwarzschild solution by using different Killing vector fields in the 5-dimensional Kaluza-Klein metric.
Gauge Systems With Noncommutative Phase Spacevcuesta
This document describes gauge systems with noncommutative phase spaces. It introduces several models of gauge systems where the phase space has a noncanonical symplectic structure involving parameters that encode noncommutativity among coordinates and momenta.
As an example, it considers a noncommutative version of the usual SL(2,R) model where the symplectic structure is modified by a parameter θ that introduces noncommutativity between one set of coordinates. The constraints of the original model are also modified to maintain the same gauge algebra. The dynamics of this noncommutative SL(2,R) model involve additional terms depending on θ.
More generally, the paper shows it is possible to construct gauge systems where non
Gauge Invariance Of The Action Principle For Gauge Systems With Noncanonical ...vcuesta
This document discusses gauge invariance of the action principle for gauge systems with noncanonical symplectic structures. It shows that for such systems, the complete set of commuting observables at the time boundary is now fixed by the boundary term and the symplectic structure, rather than just the canonical symplectic structure. The theory is applied to two nontrivial models with SL(2,R) and SU(2) gauge symmetries whose phase spaces have new interactions due to noncanonical symplectic structures.
Cartans Equations Define A Topological Field Theory Of The Bf Typevcuesta
Cartan's first and second structure equations, along with the first and second Bianchi identities, can be interpreted as equations of motion for the tetrad, connection, and two-form fields T and R. This defines a topological field theory of the BF type in four dimensions. Adding Einstein's equations relates the topological theory to general relativity. Therefore, the relationship between general relativity and topological BF theories exists already in the first-order formulation of general relativity.
Topological Field Theories In N Dimensional Spacetimes And Cartans Equationsvcuesta
This paper presents action principles for topological field theories in n-dimensional spacetimes inspired by Cartan's structure equations. The actions involve vielbeins, connections, and auxiliary fields. A canonical analysis shows the theories are topological. As an example, a 2-dimensional theory with local degrees of freedom resembling gravity coupled to matter is constructed by imposing constraints, destroying the topological character. The formalism provides a framework for geometric theories in n-dimensions and constructing modifications of gravity.
Topological Field Theories In N Dimensional Spacetimes And Cartans Equations
Cuesta Computer With Software Based On Binary Arithmetic And A Hardware Based On Bites I
1. Cuesta Computer with Software based on Binary Arithmetic and a
Hardware based on Bites I
Vladimir Cuesta †
Instituto de Investigaciones en Matem´ ticas Aplicadas y en Sistemas, Universidad Nacional Aut´ noma de
a o
M´ xico, 20-726, Ciudad de M´ xico, M´ xico;
e e e
Instituto de Ciencias Nucleares, Universidad Nacional Aut´ noma de M´ xico, 70-543, Ciudad de M´ xico,
o e e
M´ xico
e
Abstract. I present a computer with name Cuesta Computer with a Software based on Binary Arithmetic
and a Hardware based on Bites I, the set of programs or software are based on the important result of number
theory that every positive integer can be represented in an unique way on an arithmetic of base two, I represent
numbers based on the previous result and I can define a set of symbols using in a correct way the same result of
uniqueness, the hardware or the physical part of the computer consists of a band where I print or I write zeros,
ones or nothing (empty spaces), the basic units of my bands are bites.
1. Introduction
In our days, the desing and the construction of high technology computers, printers, video camera,
photographic camera and so on need mathematical tools for creating better models that the consumer
can use in their daily life, in complex applications people use clusters or supercomputers to study
physical phenomena in quantum mechanics, classical mechanics, chaos theory, the climate, storms, wind,
aeronautic engineering, construction, economics, genetics, astronomical phenomena, artificial intelligence,
cryptography, genetic algorithms, robots, industrial robots and so on (see [1], [2] and [3] for a review of the
subject). The advantage of my desing lies in the use of the available space, I think that the use of bites like
basic units is better than bytes.
2. Binary arithmetic and the representation of numbers
I present binary arithmetic with the help of a general theory and examples.
†
vladimir.cuesta@nucleares.unam.mx
2. Cuesta Computer with Software based on Binary Arithmetic and a Hardware based on Bites I 2
2.1. Binary system, basic operations
Let a be a positive integer, this number can be expressed like the unique following sum (see [4] for instance),
a = λn 2n + λn−1 2n−1 + λ1 21 + λ0 20 , (1)
where λi can take the values 0 or 1, i = 0, . . . , n, I will represent this number in the way,
λn λn−1 . . . λ1 λ0
I will call this a binary representation for the number a. It is easy to describe how to obtain this
representation. I show the following example: take the number 17, this is an odd number, take an unit
(I mean, make the operation 17 − 1 = 16 ) and write this on a square,
1
later, take 16/2 = 8, in this case I obtain an even number, then I must write a zero to the left of the previous
square. I mean,
0 1
if I continue, I must take 8/2 = 4 and is an even number and I write a zero to the left of the previous set of
squares,
0 0 1
the following step is to take 4/2 = 2 and is and even number, then I write,
0 0 0 1
the final step is to take 2/2 = 1 and I must write 1 to the left of all numbers and in fact I must finish my
reasoning when I obtain the number one in the algorithm then the number 17 can be represented like,
1 0 0 0 1
or
17 = 1 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 1 × 20 , (2)
I can sum two binary numbers following the rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1 and 1 + 1 = 0, but in
this case I must transfer one number 1 to the left, for example,
101 + 111 = 1100, (3)
another example is,
100101 + 11001 = 111110, (4)
and again I understand the number like a number with base two.
3. Cuesta Computer with Software based on Binary Arithmetic and a Hardware based on Bites I 3
Now, I show the product algorithm for numbers with base two, I can obtain 1011 × 110 in the way,
1 0 1 1
× 1 1 0
− − −− − − −
0 0 0 0
1 0 1 1
1 0 1 1
− − −− − − −
1 0 0 0 0 1 0
I finish my discussion here, but this can help to make further progress in computing with complex
technology. I mean, with electronic devices.
3. The computer
In the present section I use the mathematical theory of binary arithmetic to construct a new machine that I
called Cuesta Computer with a Software based on Binary Arithmetic and a Hardware based on Bites
I, I show my convention for programming on it.
3.1. Conventions: numbers
According to the previous section, I can think computing like a science based on binary arithmetic
(arithmetic of base two). In fact, every positive integer can be represented in an arithmetic of base two
(see [5] and [4] for instance) in an unique way, if I use this result, I can represent these kind of numbers in
a serie of powers of the number two, I show more examples,
0→ 0
1→ 1
2→ 1 0
3→ 1 1
4→ 1 0 0
5→ 1 0 1
6→ 1 1 0
7→ 1 1 1
8→ 1 0 0 0
9→ 1 0 0 1
4. Cuesta Computer with Software based on Binary Arithmetic and a Hardware based on Bites I 4
10 → 1 0 1 0
11 → 1 0 1 1
12 → 1 1 0 0
13 → 1 1 0 1
14 → 1 1 1 0
15 → 1 1 1 1
16 → 1 0 0 0 0
17 → 1 0 0 0 1
18 → 1 0 0 1 0
19 → 1 0 0 1 1
20 → 1 0 1 0 0
35 → 1 0 0 0 1 1
2001 → 1 1 1 1 1 0 1 0 0 0 1
10035833 → 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1
and so on.
3.2. Conventions: symbols
If I apply the result that I used in the previous section, I can represent a set of symbols in an unique way.
In this case I put two empty spaces before a number and I put one empty space to the final, I choose one
convention, although I can use many of them,
a→ 0
b→ 1
c→ 1 0
d→ 1 1
e→ 1 0 0
f→ 1 0 1
g→ 1 1 0
h→ 1 1 1
i→ 1 0 0 0
j→ 1 0 0 1
7. Cuesta Computer with Software based on Binary Arithmetic and a Hardware based on Bites I 7
!→ 1 0 0 0 1 0 0
Empty space ” ”→ 1 0 0 0 1 0 1
and so on.
4. Entry and exit in the computer (in and out): examples
4.1. First case: Two consecutive symbols
If I put together (entry),
1 0 1 0 0 0 1 1 1 1
I find,
1 0 1 0 0 0 1 1 1 1 → No
and If I use my convention, I find the word No, in this first case it is important to note that when I put two
symbols together it appears three empty spaces in the middle of the set of numbers, the previous sequence
occupies 16 bites or equivalently 2 bytes.
4.2. Second case: One symbol and one number
If I put together the following sequence,
1 1 0 1 1 1 1 0 1
I find,
1 1 0 1 1 1 1 0 1 → −5
and if I use my convention, I obtain -5, in this case it is important to note that when I put one symbol and
one number it appears one empty space in the middle of the set of numbers, the previous sequence occupies
12 bites or 1 byte and 4 bites.
4.3. Third: One number and one symbol
If I write one number and one symbol,
1 1 0 0 1 1
I obtain,
1 1 0 0 1 1 → 1s
and I can read 1s, in this case it is important to note that when I put one number and one symbol it appears
two empty spaces in the middle of the set of numbers, the previous sequence occupies 9 bites or equivalently
1 byte and 1 bite.
8. Cuesta Computer with Software based on Binary Arithmetic and a Hardware based on Bites I 8
4.4. Example number four
I will consider a larger example, If I put together,
1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1
1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1
0 1 1 0 0 1 0 0 0 1 0 1
0 1 0 0 0 1 0 1 1 0 1 1 1 1
1 1 0 0 1 0 0 0 0 1 0 1 0 1
1 0 1 0 0 1 0 0 1 0 0 1 0
1 0 0 0 0 0 0
I obtain,
1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1
1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1
0 1 1 0 0 1 0 0 0 1 0 1 0
1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0
1 0 0 0 0 1 0 1 0 1 1 0 1 0 0
1 0 0 1 0 0 1 0 1 0 0 0 0 0 0
Hi, I am a computer. (5)
I obtain Hi, I am a computer.
If I read from left to the right, I begin with two empty spaces. I mean, I begin with a word, If I
continue I will find three spaces and according to the previous discussion the following set of zeros and
ones represent another word, If I continue I will find three empty spaces and the next set of zeros and ones
represents one word and so on.
4.5. Example number five
If I put together the following set of bands,
1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0
1 0 0 1 1 1 0 0 0 0 0 1
I obtain,
1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0
1 0 0 1 1 1 0 0 0 0 0 1 1 + 18 = 19,
9. Cuesta Computer with Software based on Binary Arithmetic and a Hardware based on Bites I 9
and I can read 1 + 18 = 19, with this I finish my examples, but let me say a little more. If I read the total
band from left to the right I begin with a set of numbers and according to my convention I begin with a
number, the following set of empty spaces consist of two spaces, then the following object is a symbol, If
I continue I will find one empty space, then I will find a number and I can continue reading my band in a
predictable way.
5. Conclusions and perspectives
In the present paper I have presented a computer, it has the advantage that I can define in an unique way
numbers and using a convention where I can represent symbols in an unique way, too. Another important
point is that I can make programs saving my files in bites, not in bytes like people usually make and like
the reader can see this procedure permits to save files in little space. In fact, this is just the first step of
many of them because like the specialist can note, people can construct complex computer. I mean, digital
computers using my desing and in this case, all the programs must be based in a binary arithmetic, like I
did. The desing of digital technology, compilers, programs and so on it is part of future work, and like I said
my desing is better because it permits the use of less physical space, I recommend make some lectures (see
[2], [1] and [3] for citing some of them), the computer specialist can use another conventions for symbols
or some variations of my design, and this is the future work.
Acknowledgments
I appreciate all the comments of my brothers, my children and their mothers and all my family and
friends I want to dedicate this work to the interested reader in computing I hope that this paper can help
to the specialist in complex computer. I mean, for the computer and supercomputer worker, I have contact
with people working in some high technology companies and I want to name and to send greetings for some
of these high tech companies: Cray Research, Cray Incorporated, Silicon Graphics International, The Open
Group and specially to the UNIX group and so on.
References
[1] Harris, John W., Stocker Horst, Handbook of mathematics and Computacional Science, New Haven, Connecticut and
Frankfurt, Germany, Springer-Verlag (1998),
[2] Manna, Zohar, Mathematical Theory of computation Stanford University, Dover (1974).
[3] Alan Mathison Turing, Computing machinery and intelligence, Mind. 59, 433-460, (1950).
[4] William J. LeVeque, Elementary theory of numbers, University of Michigan, Dover Publications, Inc., (1990).
[5] Vladimir Cuesta, Monoids, computer science and evolution, (2010).