1. Number Systems - Part A - Digital Electronics - Vol 1
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1. Number Systems - Part A

1. Number Systems - Part A

The study of number systems is crucial for understanding how data is represented in digital systems, including computers. The chapter discusses various number systems such as decimal, binary, octal, and hexadecimal, along with their characteristics, advantages, and methods for conversion between systems. It emphasizes the importance of both analogue and digital representations and provides insights into floating-point notation for representing a wide range of numbers.

32 sections

Sections

Navigate through the learning materials and practice exercises.

  1. 1.1
    Number Systems

    This section covers various number systems, including decimal, binary,...

  2. 1.1.1
    Analogue Versus Digital

    This section distinguishes between analogue and digital representations of...

  3. 1.1.2
    Introduction To Number Systems

    This section introduces the fundamental concepts of number systems,...

  4. 1.1.3
    Decimal Number System

    The decimal number system, a radix-10 system, uses ten specific digits to...

  5. 1.1.4
    Binary Number System

    The binary number system is essential for digital electronics, using only...

  6. 1.1.4.1

    The binary number system provides significant advantages for digital...

  7. 1.1.5
    Octal Number System

    The octal number system is a base-8 numbering system, using the digits 0-7...

  8. 1.1.6
    Hexadecimal Number System

    The hexadecimal number system is a base-16 system that simplifies binary...

  9. 1.1.7
    Number Systems – Some Common Terms

    This section covers essential terms related to various number systems such...

  10. 1.1.7.1
    Binary Number System

    The binary number system is a radix-2 system with the digits 0 and 1,...

  11. 1.1.7.2
    Decimal Number System

    The decimal number system is a radix-10 system that utilizes ten digits...

  12. 1.1.7.3
    Octal Number System

    The octal number system is a base-8 numeral system using digits from 0 to 7,...

  13. 1.1.7.4
    Hexadecimal Number System

    The hexadecimal number system is a base-16 numeral system that simplifies...

  14. 1.1.8
    Number Representation In Binary

    This section discusses different methods of representing both positive and...

  15. 1.1.8.1
    Sign-Bit Magnitude

    The Sign-Bit Magnitude representation method encodes decimal numbers in...

  16. 1.1.8.2
    1’s Complement

    The 1's complement representation allows for the encoding of negative...

  17. 1.1.8.3
    2’s Complement

    The 2's complement method represents signed integers in binary, allowing for...

  18. 1.1.9
    Finding The Decimal Equivalent

    This section explains how to find the decimal equivalent of numbers in...

  19. 1.1.9.1
    Binary-To-Decimal Conversion

    This section explains how to convert binary numbers into decimal form,...

  20. 1.1.9.2
    Octal-To-Decimal Conversion

    This section focuses on the process of converting octal numbers to their...

  21. 1.1.9.3
    Hexadecimal-To-Decimal Conversion

    This section introduces the process of converting hexadecimal numbers to...

  22. 1.1.10
    Decimal-To-Binary Conversion

    This section explains the method for converting decimal numbers to their...

  23. 1.1.11
    Decimal-To-Octal Conversion

    This section outlines the method for converting decimal numbers to octal...

  24. 1.1.12
    Decimal-To-Hexadecimal Conversion

    This section covers the process of converting decimal numbers to hexadecimal...

  25. 1.1.13
    Binary–octal And Octal–binary Conversions

    This section covers the processes for converting between binary and octal...

  26. 1.1.14
    Hex–binary And Binary–hex Conversions

    This section explores the methods for converting hexadecimal numbers to...

  27. 1.1.15
    Hex–octal And Octal–hex Conversions

    This section explains the methods for converting numbers between hexadecimal...

  28. 1.1.16
    The Four Axioms

    The Four Axioms summarize the principles of converting numbers between...

  29. 1.1.17
    Floating-Point Numbers

    Floating-point notation efficiently represents a wide range of large and...

  30. 1.1.17.1
    Range Of Numbers And Precision

    This section discusses how the range of numbers and precision in...

  31. 1.1.17.2
    Floating-Point Number Formats

    Floating-point format allows for the representation of a wide range of...

  32. 1.2
    Digital Electronics

    This section explores various number systems fundamental to digital...

What we have learnt

  • Different number systems are used to represent data in digital electronics.
  • The principles of conversion between number systems are essential for understanding data representation.
  • Floating-point notation allows for the representation of both large and small numbers effectively.

Key Concepts

-- Radix
The number of different digits used in a number system, indicating its base.
-- Binary Number System
A radix-2 system using two symbols, 0 and 1, to represent numerical values.
-- FloatingPoint Notation
A method to represent real numbers that accommodates a wide range of values through the use of a significand and exponent.

Additional Learning Materials

Supplementary resources to enhance your learning experience.