## Sunil Tanna |

Sunil Tanna
Computing BooksBinary, Octal & Hexadecimal Binary (Advanced) Computing Resources: Binary, Octal & Hexadecimal
Math BooksAddition: Adding on Your Fingers Addition: Column Addition Arithmetic Sequences Fractions Long Multiplication: Grid Method Math Magic Multiplication Times Tables Platonic Solids Powers, Exponents, Indices & Surds Radians & Steradians Repeating Decimals Basic Math Resources: Algebra Addition Decimals Division Fractions Long Multiplication Powers, Exponents, Indices & Surds Times Tables Intermediate/Advanced Math Resources: Archimedean & Catalan Solids Binary & Number Bases Interesting Numbers Johnson Solids Kepler-Poinsot Polyhedra Platonic Solids Quadratic Equations Repeating Decimals Sequences Simultaneous Equations Radians & Steradians Trigonometry Extras More Math Magic Printables for Math Magic
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Below are details of my book, "Advanced Binary for Programming & Computer Science: Logical, Bitwise and Arithmetic Operations, and Data Encoding and Representation". - If you have already read the book, or want other/more advanced resources, please click here.
If you haven't already read, I have also written an introductory book
Binary, Octal and Hexadecimal for Programming and Computer Science.
- This book is now available both as a paperback book, and for the Kindle (electronic book - eBook).
- If you would like to read the Kindle (eBook) version, but don't have a Kindle reader, then you need to install the Kindle app software on your PC/Mac/iPad/etc., and then search for the book within the app. Here are some instructions for installing the Kindle software on your PC.
Advanced Binary for Programming & Computer Science: Logical, Bitwise and Arithmetic Operations, and Data Encoding and Representation
This book explains how the binary number system works and how it is used by digital computers to represent information including positive and negative integers, characters and real numbers. It also explains logical and bitwise operations that computers use to manipulate information and perform arithmetic. Finally, 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 by this book include: - What are number bases (also known as radixes).
- What is binary (base 2).
- What is octal (base 8) and hexadecimal (base 16).
- How to convert binary numbers to denary (base 10).
- How to convert denary numbers to binary.
- How binary digits (bits) are grouped into words and bytes.
- The definition of a byte.
- The definition of a word.
- The meaning of Least and Most Significant Bits.
- LSB 0 and MSB 0 conventions for numbering bits.
- The definition of a nybble.
- The correspondence between a nybble and a hexadecimal digit.
- Nybbles can be used to store denary/decimal digits in BCD representations.
- Word alignment restrictions.
- The effect of word alignment on packing and padding of data structures.
- Why there may be a need to repack data structures.
- Packing data structures and the trade-off they involve.
- The meaning of Least and Most Significant Byte.
- Byte ordering and endianness.
- What little-endian means.
- What big-endian means.
- What middle-endian means.
- What is bi-endianness.
- Fundamentals of Boolean algebra, logic gates and truth tables.
- The Boolean NOT operation.
- The Boolean AND operation.
- The Boolean OR operation.
- The Boolean XOR operation.
- The Boolean NAND operation.
- The Boolean NOR operation.
- The Boolean NXOR operation.
- Combining logic gates to create other logical operators.
- NAND and NOR are functionally complete.
- What is NAND logic.
- How to implement NOT using NAND logic.
- How to implement AND using NAND logic.
- How to implement OR using NAND logic.
- Two ways to implement XOR using NAND logic.
- How to implement NOR using NAND logic.
- The difference between logical and bitwise operations.
- How to use bitwise operations to ensure particular bits are set.
- How to use bitwise operations to invert (flip) particular bits.
- How to use bitwise operations to ensure particular bits are clear.
- How to use bitwise operations to test particular bits.
- Column addition of binary integers.
- How to implement binary addition using logic gates.
- What is and how to create a half adder.
- What is and how to create a full adder.
- How to connect multiple adders to create a ripple-carry adder.
- Performance limitations of ripple-carry adders.
- Column subtraction of binary integers.
- How to implement binary subtraction using logic gates.
- What is and how to create a half subtractor.
- What is and how to create a full subtractor from two half subtractors.
- Multiple subtractors can be connected to subtract multi-bit numbers.
- What is a left bit shift operation.
- How left shifts are usually equivalent to multiplying by two.
- How left shifts can result in numeric overflows.
- How to test for numeric overflows in left shifts.
- How to set the new least significant bit in left shifts.
- What is a right bit shift operation.
- How right shifts are usually equivalent to dividing by two and rounding down.
- How to test for rounding in right shifts.
- How to set the new most significant bit in right shifts.
- Left and right circular bit shifts.
- How to multiply by powers of 2.
- Column multiplication of denary and binary numbers.
- Russian peasant multiplication algorithm.
- Performing multiplications in hardware.
- How to divide by powers of 2.
- Comparing denary and binary long division.
- Why binary long division is easier than denary long division.
- How to create an algorithm for binary long division.
- Performing division in hardware.
- How computers represent characters in memory.
- How ASCII character-encoding works.
- Why different systems interpret ASCII differently.
- Issues with transferring ASCII text files between different types of computer systems.
- Extended ASCIIs.
- How EBCDIC character-encoding works.
- The Unicode system.
- The various Unicode character-encoding systems including UCS-2, UTF-32, UTF-16 and UTF-8.
- How UTF-16 encodes characters into 2 or 4 bytes.
- How UTF-8 encodes characters into 1, 2, 3 or 4 bytes.
- How strings of characters are represented in computer memory.
- How terminated strings including byte-terminated, null-terminated, and bit-terminated strings work.
- How length-prefixed strings work.
- Advantages and disadvantages of terminated strings versus length-prefixed strings.
- Why other types of string representations are sometimes used.
- How text mode displays store information about screen contents.
- How bitmap displays store information about screen contents.
- The purpose of parity checking and parity bits.
- The meaning of even parity.
- The meaning of odd parity.
- The advantages, disadvantages and limitations of parity checking.
- Parity's use in RAID storage devices.
- The meaning of a stick parity bit.
- The meaning of a mark parity bit.
- The meaning of a space parity bit.
- How computers represented signed numbers.
- What is offset binary representation.
- What is signed magnitude representation.
- What is one's complement.
- What is two's complement.
- What is base -2.
- What is signed-digit representation.
- How real numbers can be represented using fixed point representation.
- How real numbers can be represented using floating point representation.
- What is IEEE 754.
- What is the rational data type.
- How real numbers can be represented using logarithmic number systems.
- What are decimal computers.
- Why use denary representations of real numbers.
- What is serial decimal.
- What is two-out-of-five encoding.
- What is bi-quinary encoding.
- What are character-based encodings of denary.
- What is Binary-Coded Decimal (BCD).
- What are the NBCD (8421), 4221 and 7421 variants of BCD.
- What is Chen-Ho encoding.
- What is Densely Packed Decimal (DPD).
- What is Excess-3.
- What are decimal data-types.
- Which numbers can be exactly represented in binary fixed-point and floating-point representations.
- Which numbers can be exactly represented in decimal fixed-point and floating-point representations.
- How inexact can binary fixed-point and floating-point representations be.
- What issues does inexact representation cause.
- What is decimal representation (including decimal floating-point representation).
- What are composite data-types (structs) and how are they stored in memory.
- What are arrays and how are they stored in memory.
- What are linked lists.
- The differences singly linked-lists and doubled-linked lists.
- Possibilities for more complex data-structures.
- Types of computer memory used in early computers.
- What is magnetic-core memory and core rope memory.
- What is RAM memory.
- What are the different types of RAM memory.
- What is ROM memory.
- What are the different types of ROM memory.
- The difference between sequential and random-access secondary storage devices.
- What is punched tape storage.
- What is magnetic tape storage.
- What is magnetic disk storage.
- How data is organized into tracks, sectors and clusters on magnetic disks.
- What is the difference between hard disks and floppy disks.
- What is optical disk storage.
- What are the different types of optical disks.
- What are solid state drives and flash memory secondary storage.
- What is cloud storage.
- How memory and storage is measured.
- What is serial data communication.
- What are the advantages and disadvantages of using serial communications.
- What is the difference between Least Significant Bit first and Most Significant Bit first serial communication protocols.
- What is parallel data communication.
- What are the advantages and disadvantages of using parallel communications.
- How data transfer rates are measured.
- What is Baud.
- What is the difference between bit/second and Baud/second.
Paperback Book**Click here to get it from Amazon.com**(US and International readers)
**Click here to get it from Amazon.com**(UK readers)
eBook (Electronic Book) - Available for KindleThis book has been specially prepared for use on the Kindle - including taking great care to ensure all math symbols, formulas, and calculations display correctly on the Kindle screen (many other math books do not display math symbols correctly). A color screen is recommended, but not essential - there are a couple of diagrams where the text refers to colors in the picture - but these should still be understandable even on a black and white screen. **Click here to get it from Amazon.com**(US and International readers)
**Click here to get it from Amazon.co.uk**(UK readers)
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