Class-7th Number system

Class-7th ( 15 April 2025) 

Ch-1 .Number System 

A. Answer the following question in short.

Q.1      How many types of  number system are there in computer. 

Ans:-     There are four types of number system:-    

 1. Decimal  Number System     2. Binary  Number System     3. Octal  Number System     4. Hexadecimal  Number System 

Q.2     Convert binary number ( 11110) ₂  into decimal number (?)₁₀   

Ans:-        ( 11110) _{2 =}  ( ? )₁₀  

Q.3    Convert  decimal number ( 9 )₁₀ into binary number ( ? ) ₂

Ans:- 

            

  Q.4   What is base of Binary, Decimal , Octal & Hexadecimal number system ? 

Ans:-     Number System                         Base 

                Binary                                          2

                Decimal                                        10

                Octal                                             8

               Hexadecimal                                16 

Q.5          Solve this binary addition 

    i)    (1 0 0 0)  + (0 1 1 1)

                Ans :-    1 0 0 0                            

                            + 0 1 1 1 

                               1 1 1  1

ii)     (1 1 1 1 1)     +   (0 1 0 1 1)

Ans:-              1    1    1    1        ------- carry over 

                        1   1    1     1     1

                  +   0    1    0    1    1

                      1 0    1    0    1    0

B. Answer the following question in long.

Q.1    What is a number system ? describe different type of system.

Ans   A number system is a method for expressing and representing numbers. The most  commonly used number system are Decimal, Binary, Octal and Hexadecimal. Each of these systems has its own set of  digits and the total number of digits used in a system is called base or radius. The base is written as a subscript after the number.

Q.2    What is the octal number system and why is  it helpful in computer?

Ans:-   The octal number system is a types of counting system that uses a base of  8. It has eight digits 0, 1, 2, 3, 4 .5, 6 and 7 any number in this  system can be written using these  eight digits .Octal system is also a positional number system 

Q.3    Differentiate between hexadecimal and decimal ?

Ans:-   Hexadecimal -The hexadecimal number system is a number system with a base value  of 16 this system uses 16 symbols ; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,  a,b, c, d, e,and f . The  letter a ,b, c, d, e,  and f represent the decimal values 10, 11, 12, 13, 14, and 15 respectively.

Decimal - The decimal number system is composed of digits from 0 to 9 these ten digits can be combined in various ways to create  a wide range of  number for example some decimal number include  509 , 127 and 542 the base of the decimal number system 10 as there are 10 digits available ( 0 to 9) .

Q.4    How do you convert a binary number to decimal?

Ans  :-     Step-1. Begin with the rightmost digit of the binary number .Assign  powers of 2 to each digit, starting from 0 for the rightmost digit and increasing by 1 as you move to the left .

Step.2-    Multiply each binary digit by 2 raised  to the power of its corresponding position .

Step. 3-    Add all the resulting values . the sum of these values is the decimal equivalent of the binary  number .

Q.5    Write  Binary number for Hexadecimal   (1 to 15 )

Ans    Hexadecimal       Binary 

                   0                          0000

                   1                          0001

                   2                          0010

                   3                          0011

                   4                          0100    

                  5                          0101

                   6                          0110

                  7                          0111 

                   8                         1000

                  9                          1001   

               A( 10 )                  1010

               B( 11 )                  1011 

               C( 12 )                 1100              

               D ( 13 )              1101

               E ( 14 )               1110

               F ( 15 )              1111