BlogNCERTNCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 6

NCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 6

NCERT Solutions for Class 9th Maths Chapter 1 Number Systems Exercise 1.3 Question 6

Number Systems

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    Decimal

    Here’s the decimal number system as an example:
    digits (or symbols) allowed: 0-9
    base (or radix): 10
    the order of the digits is significant

    345 is really
    3 x 100 + 4 x 10 + 5 x 1
    3 x 10^2 + 4 x 10^1 + 5 x 10^0
    3 is the most significant symbol (it carries the most weight)
    5 is the least significant symbol (it carries the least weight)
    Binary

    Here’s a binary number system:
    digits (symbols) allowed: 0, 1
    base (radix): 2

    each binary digit is called a BIT

    the order of the digits is significant

    numbering of the digits
    msb lsb
    n-1 0
    where n is the number of digits in the number

    msb stands for most significant bit
    lsb stands for least significant bit

    1001 (base 2) is really
    1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0
    9 (base 10)

    11000 (base 2) is really
    1 x 2^4 + 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0
    24 (base 10)

    Of interest: most assembly languages have no way to represent
    binary values!
    Octal

    Here’s an octal number system:
    digits (symbols) allowed: 0-7
    base (radix): 8

    the order of the digits is significant

    345 (base 8) is really
    3 x 8^2 + 4 x 8^1 + 5 x 8^0
    192 + 32 + 5
    229 (base 10)

    1001 (base 8) is really
    1 x 8^3 + 0 x 8^2 + 0 x 8^1 + 1 x 8^0
    512 + 0 + 0 + 1
    513 (base 10)

    Hexadecimal

    here’s a hexadecimal number system:
    digits (symbols) allowed: 0-9, a-f
    base (radix): 16

    the order of the digits is significant

    hex decimal binary
    0 0 0000
    1 1 0001
    .
    .
    .
    9 9 1001
    a 10 1010
    b 11 1011
    c 12 1100
    d 13 1101
    e 14 1110
    f 15 1111

    a3 (base 16) is really
    a x 16^1 + 3 x 16^0
    160 + 3
    163 (base 10)

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