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    What Are The Number Systems

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    kainnat naeem
    Computer systems use different number systems to represent numeric values in memory and for processing. The main number systems are binary, octal, decimal, and hexadecimal. Binary uses only the digits 0 and 1. Octal uses digits 0-7. Decimal uses 0-9. Hexadecimal uses 0-9 and A-F to represent values. Numbers can be converted between these systems through division and remainder operations or by multiplying each digit by its place value and summing the results.

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    What Are The Number Systems

    Uploaded by

    kainnat naeem
    144 views3 pages
    Computer systems use different number systems to represent numeric values in memory and for processing. The main number systems are binary, octal, decimal, and hexadecimal. Binary uses only the digits 0 and 1. Octal uses digits 0-7. Decimal uses 0-9. Hexadecimal uses 0-9 and A-F to represent values. Numbers can be converted between these systems through division and remainder operations or by multiplying each digit by its place value and summing the results.

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    What are the number systems

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    Computer systems use different number systems to represent numeric values in memory and for processing. The main number systems are binary, octal, decimal, and hexadecimal. Binary uses only the digits 0 and 1. Octal uses digits 0-7. Decimal uses 0-9. Hexadecimal uses 0-9 and A-F to represent values. Numbers can be converted between these systems through division and remainder operations or by multiplying each digit by its place value and summing the results.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    144 views3 pages

    What Are The Number Systems

    Uploaded by

    kainnat naeem
    Computer systems use different number systems to represent numeric values in memory and for processing. The main number systems are binary, octal, decimal, and hexadecimal. Binary uses only the digits 0 and 1. Octal uses digits 0-7. Decimal uses 0-9. Hexadecimal uses 0-9 and A-F to represent values. Numbers can be converted between these systems through division and remainder operations or by multiplying each digit by its place value and summing the results.

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    of 3

    What are the number systems 

    in Computer?
    Number systems are the technique to represent numbers in the computer
    system architecture, every value that you are saving or getting into/from
    computer memory has a defined number system.

    Computer architecture supports following number systems.

     Binary number system


     Octal number system
     Decimal number system
     Hexadecimal (hex) number system

    1) Binary Number System


    A Binary number system has only two digits that are 0 and 1. Every number
    (value) represents with 0 and 1 in this number system. The base of binary number
    system is 2, because it has only two digits.

    2) Octal number system


    Octal number system has only eight (8) digits from 0 to 7. Every number (value)
    represents with 0,1,2,3,4,5,6 and 7 in this number system. The base of octal
    number system is 8, because it has only 8 digits.

    3) Decimal number system


    Decimal number system has only ten (10) digits from 0 to 9. Every number (value)
    represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal
    number system is 10, because it has only 10 digits.

    4) Hexadecimal number system


    A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to
    9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E
    and F in this number system. The base of hexadecimal number system is 16,
    because it has 16 alphanumeric values. Here A is 10, B is 11, C is 12, D is 13, E is
    14 and F is 15.

    Number System Conversions


    There are three types of conversion:

     Decimal Number System to Other Base


    [for example: Decimal Number System to Binary Number System]
     Other Base to Decimal Number System
    [for example: Binary Number System to Decimal Number System]
     Other Base to Other Base
    [for example: Binary Number System to Hexadecimal Number System]

    Decimal Number System to Other Base


    To convert Number system from Decimal Number System to Any Other Base is
    quite easy; you have to follow just two steps:
    A) Divide the Number (Decimal Number) by the base of target base system (in
    which you want to convert the number: Binary (2), octal (8) and Hexadecimal
    (16)).
    B) Write the remainder from step 1 as a Least Signification Bit (LSB) to Step last
    as a Most Significant Bit (MSB).

    Other Base System to Decimal Number Base


    To convert Number System from Any Other Base System to Decimal Number
    System, you have to follow just three steps:
    A) Determine the base value of source Number System (that you want to
    convert), and also determine the position of digits from LSB (first digit’s position
    – 0, second digit’s position – 1 and so on).
    B) Multiply each digit with its corresponding multiplication of position value and
    Base of Source Number System’s Base.
    C) Add the resulted value in step-B.

    Explanation regarding examples:


    Below given exams contains the following rows:
    A) Row 1 contains the DIGITs of number (that is going to be converted).
    B) Row 2 contains the POSITION of each digit in the number system.
    C) Row 3 contains the multiplication: DIGIT* BASE^POSITION.
    D) Row 4 contains the calculated result of step C.
    E) And then add each value of step D, resulted value is the Decimal Number.

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