Decimal and Binary Number

Number System

History of number starts from primitive age of human being. The development of number system has integrated with the development of human beings. In primitive age, people used to count stones and pebbles. Hindu philosophers have developed the number system called decimal numbers. From the number various other numbers are derived and developed. These numbers are binary numbers, octal numbers, hexadecimal numbers etc.

Decimal (Denary) Numbers

The number of base or radix ten is called decimal numbers. It is first number system in which all the ancient and modern mathematical calculation is done. Other number system is derived from this number. It is generated with the combination of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can represent these numbers with suffix two. Eg (9810)10

The following chart displays relations among several number systems derived from the decimal number.

System Base 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hexadecimal 16 0 1 2 3 4 5 6 7 8 9 A B C D E F
Decimal 10 0 1 2 3 4 5 6 7 8 9
Octal 8 0 1 2 3 4 5 6 7
Binary 2 0 1

Binary Number

Binary Number is a number of two base numbers. It is represented by 1 and 0. 1 or 0 is called Binary digits.

We can generate this number with the combination of 0 and 1. It is represented with suffix two. Eg (10101)2.

Following table shows some decimal number and their equivalent binary numbers.

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001

Conversion of Binary to Decimal and vice versa

We multiply each binary digit by its weighted position, and add each of the weighted value together.

Weighted value:

25 24 23 22 21 20
32 16 8 4 2 1


To convert decimal number to binary number,repeated division by two is needed.

Convert following into binary numbers:

(45)10= (101101)2

2 45 1
2 22 0
2 11 1
2 5 1
2 2 0
1

=(101101)2

(225)10= (10111001)2

2 225 1
2 112 0
2 56 0
2 23 1
2 11 1
2 5 1
2 2 0
1

= (10111001)2

  • The arrangement of number in a computer system is known as computer number system.
  • There are different types of computer number system.They are binary number system( have base 2), octal number system(have base 8), decimal number system(have base 10 ) and hexadecimal number system(have base 16).
  • Binary Number is a number of two base numbers. It is represented by 1 and 0. 
  • The number of base or radix ten is called decimal numbers.
0%
  • According to addition rule of binary number system, 1+1 equals to:

    4


    11


    10


    2


  • According to subtraction rule of number system, 0-1 equals to:

    -1


    01


    10


    -11


  • According to multiplication rule of number system, 0*1 equals to:

    11


    10


    1


    100


  • Octal number system consists of _________.

    2 digits
    10 digits
    8 digits
    16 digits
  • A number system having two base numbers is:

    binary number system
    octal number system
    decimal number system
    hexadecimal number system
  • What is the decimal value of the binary number 111?

    8
    9
    7
    3
  • What is the decimal value of the binary number 1000?

    6
    7
    8
    9
  • What is the binary value of the decimal number 45?

    101101
    11101
    111101
    101111
  • What is the binary value of the decimal number 226?

    10111011
    11101111
    11101011
    101111
  • The number of base or radix ten is called _________.

    octal number
    hexa decimal number
    decimal number
    binary number
  • The base of decimal number system is _________.

    2
    8
    10
    5
  • The base of binary number system is _________.

    16
    10
    20
    2
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