8th Class Computers Science IT Basics Introduction to Number System          

     Introduction to Number System

The number of digits in the system determines the base of any number system, such as decimal and binary. Basically binary is a base-2 number system as it uses two basic digits. Thus it means that the whole Binary number system depends on the two basic digits. Whereas Decimal is a base-10 system since it uses ten digits, and these are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.  

  Decimal Number System

A system with base-10 is a decimal number system. Thus it means that there are ten basic digits on which the decimal number system depends. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. By using these ten digits all the numbers in decimal number system are written. Thus the place value of a digit in a number increases the power from right to left. For example, the following are the place value of each digit of number 5471: The place value of 1 is: 1*100 =1 The place value of 6 is: 7*101 =70 The place value of 3 is: 4*102 =400 The place value of 5 is: 5*103 =5000  

 Binary Number System

A number system with a base-2 is known as binary number system. The whole binary number system depends on two digits these are 0 and 1, respectively. By using these two digits the numbers in binary number system are written. Thus the place value of a digit in a number increases in the power of 2 from right to left. The following example shows the place value of each digit in the number 101010 should be 010101 The place value of 1 is: 1*20 = 1 The place value of 0 is: 0*21 = 0 The place value of 1 is: 1*22 = 4 The place value of 0 is: 0*23 = 0 The place value of 1 is: 1*24 = 16 The place value of 1 is: 0*25 = 0  

 Hexadecimal Number System

The hexadecimal number system is based on 16. It means, there are 16 basic digits on which whole hexadecimal number system depends. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,13,14 and 15, where as the numbers 10, 11,12, 13, 14 and 15 are also represented as A, B, C, D, E and F. By using these 16 digits all the numbers in Hexadecimal number system are written. Thus the place value in hexadecimal system is increased in the power of 16 from right to left. The following example shows the place value of each digit in the number 121FA: Place value of A is: 10*160 =10 Place value of F is: 15 *161 =240 Place value of 6 is: 1*162 = 256 Place value of 2 is: 2*163 =8192 Place value of 1 is: 1*164 =65536