This book is directed toward readers seeking a concise introduction to binary numbers with an inclination toward understanding computer systems. The material presented can be used as a supplement for courses relevant to computer science and computer engineering anywhere from the high school level up to the college level. Several in-chapter and end-of-chapter exercises are included in order to ensure the interested reader is able to practice and fully internalize the topics presented. Depending upon the level of the reader and the rate at which the material is covered, the book topics can be mastered within a period of two to six weeks.
Elementary students around the globe are taught to count using a base-10 number system. We form numbers using the 10 digits of our base-10 system�zero through nine. Inside this book, readers discover other number systems people have used throughout history. With a binary system, computers only use two digits�0 and 1. So how does a computer count to 10? Readers will learn the answer inside this book. Also included is a review of hexadecimal numbers, which serve as the old basis of assembly languages and can still be found today setting colors on the web. This volume meets math standards addressing number systems other than base 10.
There are many good Java programming books on the market, but it's not easy to find one fit for a beginner. This book simplifies the complexity of Java programming and guides you through the journey to effectively work under the hood. You'll start with the fundamentals of Java programming and review how it integrates with basic mathematical concepts through many practical examples. You'll witness firsthand how Java can be a powerful tool or framework in your experimentation work. Learn Java with Math reveals how a strong math foundation is key to learning programming design. Using this as your motivation, you'll be programming in Java in no time. What You'll Learn Explore Java basicsProgram with Java using fun math-inspired examplesWork with Java variables and algorithmsReview I/O, loops, and control structuresUse projects such as the Wright brothers coin flip gameWho This Book Is For Those new to programming and Java but have some background in mathematics and are at least comfortable with using a computer.
This book introduces the binary, octal and hexadecimal numbering systems used in computer science and computer programming. It introduces how numbers are represented in each of these systems, how to convert between them (and to and from base 10). In this book, among other things, you will learn: * What are number bases (also known as radixes) * What is binary (base 2) * How to convert binary numbers to denary (base 10) * How to convert denary numbers to binary * What is octal (base 8) * How to convert octal numbers to denary * How to convert denary numbers to octal * Why many programmers and computer scientists use octal * How to convert octal numbers to binary * How to convert binary numbers to octal * What is hexadecimal (base 16) * How to convert hexadecimal numbers to denary * How to convert denary numbers to hexadecimal * Why many programmers and computer scientists use hexadecimal * How to convert hexadecimal numbers to binary * How to convert binary numbers to hexadecimal * Is there a reason to prefer octal over hexadecimal or vice-versa?
This book explains how the binary works and how it is used by computers to represent information including positive and negative integers, characters and real numbers. It explains the logical and bitwise operations used to manipulate information and perform arithmetic. We also briefly look at how computers store this information in memory and secondary storage, and how it can be transmitted between computers. Topics covered include: INTRODUCING NUMBER BASES AND BINARY CONVERTING FROM BINARY TO DENARY AND VICE-VERSA How to Convert a Binary Number to Denary How to Convert a Denary Number to Binary HOW COMPUTERS GROUP BINARY DIGITS A Closer Look at Bytes A Closer Look at Words * Word alignment, word alignment and packing, byte ordering and endianness Addresses BOOLEAN OPERATIONS AND LOGIC GATES Fundamentals of Boolean Algebra * NOT, AND, OR, XOR, NAND, NOR, NXOR Combining Logic Gates * NOT, AND, OR, XOR, NOR using NAND logic Logical Versus Bitwise Operations Using Bitwise Operations to Set, Clear, Flip or Test Bits * Setting bits, inverting bits, clearing bits, testing bits ADDING AND SUBTRACTING IN BINARY Adding Binary Integers * The column addition method of adding denary numbers and adding binary numbers, implementing binary addition using logic gates Subtracting Binary Integers * The column subtraction methods of subtracting denary numbers and subtracting binary numbers, implementing binary subtraction using logic gates SHIFT OPERATIONS Left Shift Right Shift Circular Shifts MULTIPLICATION AND DIVISION IN BINARY Multiplication * Multiplying by a power of 2, column multiplication, Russian peasant multiplication algorithm, multiplication in hardware Division * Dividing by a power of 2, denary long division, binary long division, algorithm for binary long division, division in hardware REPRESENTING CHARACTERS AND STRINGS OF CHARACTERS Representing Individual Characters * ASCII, extended ASCIIs, BCDIC and other early character encodings, EBCDIC, Unicode Representing Strings of Characters * Terminated strings, length-prefixed strings, other string representations REPRESENTING TEXT AND GRAPHICS ON SCREEN Text Mode Displays Bitmap Displays PARITY CHECKING What is a Parity Bit Even and Odd Parity Advantages, Disadvantages and Limitations of Using Parity Checking Parity's Use in RAID Storage Devices Unused Parity Bits SIGNED INTEGERS Offset Binary Signed Magnitude Representation One's Complement Two's Complement Other Representations of Signed Numbers * Base -2, signed-digit representation REAL NUMBERS Fixed Point Representation Floating Point Representation Rational Data Type Logarithmic Number Systems DENARY ENCODINGS AND DECIMAL DATA TYPES Why Use Denary Representations of Real Numbers? Binary Encodings of Denary * Serial decimal, two-out-of-five, bi-quinary, character-based encodings of denary, binary-Coded Decimal (BCD), Chen-Ho Encoding, Densely Packed Decimal (DPD) and excess-3 Decimal Data Types * Which numbers can be exactly represented in fixed and floating point? * How inexact? * Issues with inexact representation * Decimal representation DATA STRUCTURES Structs Arrays Linked Lists and More Complex Structures * Limitations of arrays, introducing linked lists, singly and doubly linked lists, more complex data structures TYPES OF COMPUTER MEMORY Magnetic-Core Memory and Core Rope Memory RAM * DRAM and SRAM ROM * Mask-programmed ROM, PROM, EPROM, EEPROM, Flash memory SECONDARY STORAGE Sequential Storage * Punched tape, magnetic tape Random Access Storage * Magnetic disk, optical disk, solid state drives, flash memory and cloud Storage MEASURING MEMORY AND STORAGE DIGITAL COMMUNICATIONS Serial Communication Parallel Communication MEASURING TRANSFER RATES Baud
This book is a compilation of the entire research work on the topic of Complex Binary Number System (CBNS) carried out by the author as the principal investigator and members of his research groups at various universities during the years 2000-2012. Pursuant to these efforts spanning several years, the realization of CBNS as a viable alternative to represent complex numbers in an “all-in-one” binary number format has become possible and efforts are underway to build computer hardware based on this unique number system. It is hoped that this work will be of interest to anyone involved in computer arithmetic and digital logic design and kindle renewed enthusiasm among the engineers working in the areas of digital signal and image processing for developing newer and efficient algorithms and techniques incorporating CBNS.
The first collection of Leibniz’s key writings on the binary system, newly translated, with many previously unpublished in any language. The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today’s digital computing. This book offers the first collection of Leibniz’s most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz’s original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz’s mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz’s development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age.
