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.

According to addition rule of binary number system, 1+1 equals to:
4
11
10
2

According to subtraction rule of number system, 01 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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