Number Systems Overview
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Questions and Answers

What is the base of the hexadecimal number system?

  • 2
  • 10
  • 16 (correct)
  • 8
  • The decimal number system is used by computers for internal representation.

    False

    What is the process of converting a number from one number system to another?

    Conversion

    The value of each digit in a number system is determined by its _______________________ and base.

    <p>position</p> Signup and view all the answers

    Which of the following number systems uses digits 0-7?

    <p>Octal</p> Signup and view all the answers

    Match the following number systems with their descriptions:

    <p>Decimal = Most commonly used number system Binary = Used by computers for internal representation Octal = Used in some computer programming Hexadecimal = Used in computer programming and web development</p> Signup and view all the answers

    Study Notes

    Number Systems Overview

    A number system is a way to represent numbers using digits or symbols in a specific base or radix.

    Types of Number Systems

    • Decimal Number System (Base 10)
      • Uses digits 0-9 to represent numbers
      • Most commonly used number system
    • Binary Number System (Base 2)
      • Uses digits 0 and 1 to represent numbers
      • Used by computers for internal representation
    • Octal Number System (Base 8)
      • Uses digits 0-7 to represent numbers
      • Used in some computer programming
    • Hexadecimal Number System (Base 16)
      • Uses digits 0-9 and letters A-F to represent numbers
      • Used in computer programming and web development

    Number System Conversion

    • Conversion between number systems:
      • Decimal to Binary: Divide by 2 and keep remainder
      • Decimal to Octal: Divide by 8 and keep remainder
      • Decimal to Hexadecimal: Divide by 16 and keep remainder
    • Conversion rules:
      • Each digit in the original number system corresponds to a specific value in the new number system
      • Follow the place value system (ones, tens, hundreds, etc.) when converting

    Properties of Number Systems

    • Base (Radix): The number of unique digits used in the number system
    • Place Value: The value of each digit based on its position in the number
    • Weight: The value of each digit based on its position and base

    Number Systems Overview

    • A number system represents numbers using digits or symbols in a specific base or radix.

    Types of Number Systems

    • Decimal Number System (Base 10): • Uses digits 0-9 to represent numbers • Most commonly used number system
    • Binary Number System (Base 2): • Uses digits 0 and 1 to represent numbers • Used by computers for internal representation
    • Octal Number System (Base 8): • Uses digits 0-7 to represent numbers • Used in some computer programming
    • Hexadecimal Number System (Base 16): • Uses digits 0-9 and letters A-F to represent numbers • Used in computer programming and web development

    Number System Conversion

    • Conversion between number systems involves dividing by the base of the new system and keeping the remainder.
    • Decimal to Binary conversion: divide by 2 and keep remainder.
    • Decimal to Octal conversion: divide by 8 and keep remainder.
    • Decimal to Hexadecimal conversion: divide by 16 and keep remainder.

    Properties of Number Systems

    • Base (Radix): the number of unique digits used in the number system.
    • Place Value: the value of each digit based on its position in the number.
    • Weight: the value of each digit based on its position and base.

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    Description

    Learn about different number systems, including decimal, binary, and octal. Understand the base and digits used in each system.

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