Computer Notes Chapter- 7 Number System ! Non-Positional Number System ! Positional Number System ! Decimal Number System ! Binary Number System ! Octal Number system ! Hexadecimal Number System ! ASCII Code !

NUMBER SYSTEM 

Every Computer stores number, letter, and other special characters in coded  form, Before going into the details of these codes , it is essential to have a basic understanding of the number system.

NUMBER SYSTEM :                                                                                                                                           A number system of base (radix) r is a system, which has r distinct symbols for r digits number systems are basically of classified into, major categories: non-positioned  and positional. 

Non- Positional Number System:                                                                                                                In early days, human beings counted on fingers. When ten fingers. were not adequate, stones, pebbles or sticks were used to indicate values This method of counting uses an additive approach or the non- positional number system. In this system. we have symbols such as i for 1, II for 2, III for 3, IIII for 4 etc. each symbol represents the same value regardless of its position in the number and the symbols are simply added to fine out the value of a particular number. Since it is very difficult to perform arithmetic operating with such a number system, positional number system was developed as the centuries passed .

Positional Number System:                                                                                                                        

In a positional number system, there are only a few symbols called digits and these symbols represent different values depending on the position they in the number, The value of each digit i such a number is determined by three considerations.                                                                                                             

i. the digit Itself                                                                                                                                             ii. The position of digit in the number, and                                                                                                  iii. The bas of the number system (were base is defined as the total number of digits available in the number system)                                                                                                                

There are four types of representation of number system:                                                                          

        1. Decimal Number System                                                                                                        

2. Binary Number System                                                                                                 

3. Octal Number System                                                                                                  

  4. Hexa Decimal Number                                                                                                  

      Decimal Number System:                                                                                                                      The number system which we use in our day -to-day  life is called decimal number system, in this system, the base is equal to 10, because there are altogether ten symbols or digits (0,1,2,3,4,5,6,7,8,9)

Binary Number System:                                                                                                                              The Binary number system is exactly like the decimal number system system, except that the base is 2, instead of 10. we have only two symbols or digits (0 and 1) , which can be used in this number system.

Octal Number System :                                                                                                                               In the octal number, the base is 8 Hence, there are only eight symbols or digits 0,1,2,3,4,5,6,and 7 the largest digit 7 . Each position in an octal number represents a power of the base (8)                             

Hexadecimal Number System:                                                                                                                   The hexadecimal number system is one with a base of 16 single- character digits or symbols The first 10 digits are the digits of the decimal number system- 0,1,2,3,4,5,6,7,8,9. The remaining six digits are denoted by the symbols A,B,C,D,E and F, representing the decimal values 10,11,12,13,14 and 15, respectively.                                                                                                                                  

                                                                                                                                       

 Covert a  decimal number to binary         

                                                                              

43₁₀ = ?₂

Solution:

2	43	1
2	21	1
2	10	0
2	5	1
2	2	0
	1

 

Hence, 43₁₀ = 101011₂

Covert a Binary Number to Decimal

101011₂ =?₁₀

1x2⁵ + 0x2⁴ + 1x2³ + 0x2² +1x2¹ + 1x2⁰

32+0+8+0+2+1

43 Hence, 101011₂ =43₁₀

Decimal	Hexadecimal	Binary	Octal
0	0	0	0
1	1	1	1
2	2	10	2
3	3	11	3
4	4	100	4
5	5	101	5
6	6	110	6
7	7	111	7
8	8	1000
9	9	1001
10	A	1010
11	B	1011
12	C	1100
13	D	1101
14	E	1110
15	F	1111

 ASCII Code

 ASCII stands for American Standard Code for information Interchange. ASCII code is used extensively in small computers, peripherals, instruments and communications device, it has replaced  many of the special codes that were previously used.