NUMBER SYSTEMS

NUMBER SYSTEM

Data Storage:

We use decimal numbers for out day to day activities, the decimal numbers are 10 digits i.e from 0 to 9 but computer understands only 1’s and 0’s ( machine language) in the past we use 0’s and 1’s for numbers and the alphabets but now the alphabets, numbers and special characters are converted into 1’s and 0’s .So that the computer can understand easily. To understand the corking of a computer the knowledge of binary, octal, hexa decimal and decimal number system is essential. Basically there are 4 types of number systems.

1.       Decimal    -   ()₁₀
2.       Binary      -   ()₂
3.       Octal        -   ()₈
4.       Hexa        -   ()₁₆

Conversions:

1. Decimal to Binary
2. Binary to Decimal
3. Binary equivalent to decimal
4. Octal to Hexa
5. Hexa to Octal

Decimal                     Binary

0                              0000

1                              0001

2                              0010

3                              0011

4                              0100

5                              0101

6                              0110

7                              0111

8                              1000

9                              1001

                          

Computer Data Code: Computer accepts data and instructions in machine language, represented internally by the bits 0 and 1. In binary coding every symbol of text data is represented by a group of bits. A group of bits is called “Byte”

Bit: A smallest memory unit where we can store one(or) zero is called bit.

Modern computers use 8 bits to represent a symbol. The most popular text code systems are

1.     Binary Code Decimal (BCD)

2.     American Standard Code for Information Interchange(ASCII)

3.     Extended Binary Code Decimal Interchange Code (EBCDIC)

4.     Uni-Code

Binary code Decimal (BCD): BCD is the simplest binary code i.e. is used to represent a decimal number.

            Note: In BCD 4 bits represent a decimal number

For example the BCD equivalent of 951 is 10010101001. This conditions scheme has been extended to cover the alphabets and special symbols by adding two more bits on the left of the 4 bits.

Ex:

            Decimal                        Binary (BCD)

            0                              000000

            1                              000001

            2                              000010

            :                              :

            :                              :     

            X                              010111

            Y                              011000

            Z                              011001

Digits (10) , alphabets (26) and specials (15)

American standard Code for Information Inrechange(ASCII):

This is used extensively in small computers peripherals, instruments and communication devices. It is a 7 bit code, used to control  various devices in computer and printable control codes that represents lower and upper letters digits. With 7 bits 128 characters can be coded.

ASCII-8 Code: A new version which is 8 bit code, capacity is extended to 256 characters. This includes graphics, symbols and mathematical representation.

EBCDIC: It is a standard character code for large computers. It is an 8 bit code without purity. EBCDIC first 4 bits known as zone bits and second 4 bits known as digit value.

Decimal                              ASCII                                  EBCDIC

      1                                   00110001                              11110001

      2                                   00110010                              11110010

      3                                   00110011                              11110100

      4                                   00110100                              11110100

      5                                   00100101                              11110101

      :                                           :                                           :

      :                                           :                                           :

      Z                                  01011010                              11101001

Uni Code: It is a worldwide character code standard. In this 16 bits (2 bytes) are used to represent a character (or) symbol, using, this code system 65.536 different characters can be represented inside the computer. It was developed in 1991 by apple and Xerox Corporation.

†      Memory Range:

                        Name                        Abbreviation

                        Kilo                                 K

                        Mega                              M

                        Giga                               G

                        Tera                               T

                        Peta                                P

                        Exa                                 E

                        Zetha                              Z

                        Yotta                              Y