What is Number Systems - Introduction | Bits and Bytes | brieflynotes

 Number Systems

Introduction:

There are several kinds of data such as, numeric, text, date, graphics, image, audio and video that needed to be process to by a computer. The text usually consist of standard alphabetic, numeric, and special characters. The graphics data consist of still pictures pictures drawing and photographs. Any type of sound including music and voice, is considered as audio data. Video data consists of motion pictures. The data has to be converted into to a format that the computer data can be classified into two forms, analog data and digital data. Analogue data can have any value within a defined range and it is continuous. Sound waves, telephone signals, temperatures and all other signals that are not broken into bits are examples of analogue data. Digital data can be represented by a series of binary numbers and it is discrete.


The arithmetic and logic unit (ALU) of the computer performs arithmetic and logical operations on data. computer arithmetic is commonly performed on two different types of numbers, integer and floating point. As the hardware required for arithmetic is much simpler for integers than floating point numbers, this two types have entirely different representations. An integer is a whole number and the floating point number has a  fractional part. To understand about how computers store data in the memory and how they handle them one must know about bits and bytes and the number systems.


Bits and bytes or common computer jargons. Both the main memory (Random access memory or RAM) and the hard disk capacities are measured in terms of bytes. The Hard disk and memory capacity of a computer and other specifications or described in terms of bits and bytes. For instance, computer me be described as having a 32 bit Pentium processor with 128 megabytes of RAM and hard disc capacity of 40 gigabytes.


Bits and Bytes


A numbering system is a way of representing numbers. The most commonly used numbering system is the decimal system. Computer systems can perform computations and transmit data representations. It is important for every one studying computers to know how the binary systems and hexadecimal system work. A bit is small piece of data that is derived from the words "Binary Digit". Bits have only two possible values, 0 and 1. A binary number contains a sequence of 0s and 1s like 10111. A collection of 9 bits is called as a byte. With 8 bits in a byte, we can represent 256 values ranging from 0 to 255 as shown below.
0=0000 0000
1=0000 0001
2=0000 0010
3=0000 0011 
254=1111 1110
255=1111 111

Bytes are used to represent characters in a text. Different types of coding schemes are used to represent the character Set and numbers. The most commonly used coding scheme is the American Standard Code for Information interchange (ASCII). Each binary value between 0 and 127 is used to represent a specific character. The ASCII value for your blank character is 32 and the ASCII value of numeric 0 is 48. The range of ASCII values for lowercase alphabets is from 97 to 122 range of ASCII values for the upper case alphabets is 65 to 90. Computer memory is normally represented in terms of kilobytes or megabytes. In metric system, one kilo represents 1000, that is 103. In binary system, one kilo byte represents 1024 bytes, that is, 210. The following table shows the representation of various memory sizes.

NAME    ABBREVIATION   SIZE (BYTES)
KiloK2^10*
MegaM2^20
GigaG2^30
TeraT2^40
PetaP2^50
ExaE2^60
ZettaZ2^70
YottaY2^80
                 Read as 2 power 10

In a 2GB (Giga bytes) storage device (hard disk), totally 21,47,483,648 bytes can be stored. Nowadays, databases having size in Terabytes are reported. Zetta and Yotta size databases are yet to come.

Decimal number system

In our daily life, we use system based on digits to represent numbers. the system that uses the decimal numbers or digits symbols 0 to 9 is called as decimal number system. The system is said to have a base, or radix, of ten. sequence of digits symbol are used to represent numbers greater than 9. When a number is written a sequence of decimal digits, its value can be interpreted using the positional value of each digit in the number. The Positional number system is a system of writing numbers where the value of a digit depends not only on the digit, but also on a it's placement within a number. In the positional number system, each decimal digit is weighted relative to its position in the number. This means that each digit in the number is multiplied by ten raised to a power corresponding to that digits position. Thus the value of the decimal sequence 948 is

94810=9 X 102 + 4 X 101 + 8 X 100

Fractional values are represented in the same manner, but exponents are negative for digits on the right side of the decimal point. thus the value of the fractional decimal sequence 948.23 is

  948.2310=9 X 102 + 4 X 101 + 8 X 100 + 2 X 10-1 + 3 X 10-2

In general, for the decimal representation of

X = {....x2x1x0 . x-1x-2x-3 ......} The value of X is

X= Si x 10i where i= ...... 2, 1, 0, -1, -2, ......

 

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