Class XI | CHAPTER 3

                                         DATA REPRESENTATION

This chapter discusses decimal, binary, octal and hexadecimal number systems and physical representation of digits in computers.

DIGITAL NUMBER SYSTEMS-

DECIMAL NUMBER SYSTEMS-

The decimal system is composed of 10 numerals or symbols (Deca means 10, that’s why this system is called decimal system).

These symbols are 0,1,2,3,4,5,6,7,8,9; using these symbols as digits of a number, we can express any quantity. This system is called base-10 system.

Expanded form- (dn……d3+ d2+ d1+ . d-1+ d-2…….d-n)

Example: 25.12

 2 * 10 + 5 * 1 +1 * 1/10 +2 * 1/100.

The decimal point is used to separate the integer and fractional parts of the number.

MSD- Most significant digit

LSD- Least significant digit

BINARY NUMBER SYSTEM-

In the binary system there are only two symbols or possible digit values, 0 and 1. This is base-2 system.

Possible symbol= 0 to n-1

Example: 1010101₂

OCTAL NUMBER SYSTEM-

The octal number system is very important in digital computer work. Octal is another number system with less symbols to use than our conventional number system. Octal is fancy for Base Eight meaning eight symbols are used to represent all the quantities. They are 0, 1, 2, 3, 4, 5, 6, and 7.

Example: 73₈

HEXADECIMAL NUMBER SYSTEM-

The hexadecimal system is Base Sixteen. As its base implies, this number system uses sixteen symbols to represent numbers. Unlike binary and octal, hexadecimal has six additional symbols that it uses beyond the conventional ones found in decimal. the total list of symbols to use is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

Hexadecimal A  B   C    D   E    F

Decimal        10 11  12  13  14  15

Example: 2C9₁₆

Conversion-

Group A-

1. Binary to decimal conversion = 1010₂  = (X)₁₀

2. Octal to decimal conversion = (0 to 7)₈ = (X)₁₀

3. Hexadecimal to decimal conversion = (0 to 9, A to F)₁₆ = (X)₁₀

Group B-

1. Decimal to Binary conversion= (0 to 9)= 

2. Decimal to Octal conversion==

3. Decimal to hexadecimal conversion =  =

Group C-

1. Binary to octal.

=           

 11,111,011,110,101

  3   7      3    6     5

2. Octal to binary.

                       =    7     3

                                111   011   =

3. Hexadecimal to binary.

    =

                    F         A           C             E

                 1111   1010      1100         1110

Thus, he solution is .      

4. Binary to Hexadecimal.

 =

Group in fours          11,0111,1010,1110

Convert each no.         3   7        A     E

Thus solution is 37AE.

5. Octal to Hexadecimal.

 =

Successive division                         Remainders                                   hex notation

16) 423                                                7                                                    7

    16)26                                              10                                                  A

         16)1                                            1                                                   1

              0

Reading the remainders up from the bottom, the result is .

6. Hexadecimal to octal.

    

 = 1011  0010   1111 ( CONVERT TO BINARY)

           = 101    100     111   (GROUP BITS BY 3s)

           = 

Binary Representation of Integer

•       Sign and magnitude representation.

•       1’s compliment

•       2’s compliment

•       1’s compliment- it represents +ve number by their binary equivalent and –ve number by their 1’s compliment.

•       2’s compliment represents +ve number in true form and –ve in 2’s compliment

•       ASCII- American Standard code for Information Interchange.

•       Real numbers are represented by their exponents and mantissa