The use of different symbols by different bases means that a no. system uses 10 different symbols and from the 11th no. the cycle of symbol repeats. The concept bases have long existed. Earlier for each of the counted nos. a different symbol was used. However the problem with this system was as the list of the no. counted increased so did the no. of symbols that were used. In fact there would be infinite no. of symbols if this system was followed. This problem was recognized early on by the human civilization and the concept of bases was introduced. Egyptians used a base of 2, Babylonians base of 60, for Mayans the base was 18 and 20. Currently however the number system that is mostly used is the decimal no. system with base 10. The different no. systems that are generally used by computers are:
Decimal- This is the no. system which has a base of 10. The lists of symbols of decimal no. system are 0,1,2,3,4,5,6,7,8,9 and after 9 the counting again starts from 1. The symbols in a decimal system range from 0 to 9. So after 9 are reached the system should start from 1. But if the system starts from 1 then it will be difficult to understand. So an empty placeholder should be placed in the one’s place. A symbol which is part of the list of symbols, doesn’t have a value in itself but signifies great value when places along with another no. This job is done by the symbol 0. Hence after reaching 9 the system starts from 10.
Binary- The binary no. system is the no. system that is most commonly used and understood by the computers. Binary no. system has only 2 symbols 0 and 1 (Merlot, 2002). 0 and 1 are the two states that are represented by on and off. On state represents 1 and off state represents 0. For writing a no. in the binary no. system the way is to write the no. in the parenthesis and then attach a base 2 as subscript after closing parenthesis is written. For example to write (25)10 in binary no. system, it is written as (11001)2.
Octal- The octal no. ...Show more