Binary Number System

Binary Number System

The Computers understands only Binary Number System . And therefore we need to communicate with computers only using Binary Code ( Machine Language ). In this lesson we will discuss and find answers to why computers understand only Binary code which consist of only two numbers that is 0 and 1.

Binary Numbers - Table Of Contents

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What Is Number System ?

We are all familiar with the commonly used numerical number system ( Decimal Number System that makes use of digits from 0 to 9 )  that we all use in our daily life . However there are many  number system exist that can be used while communicating with the computer system and supported by most computer programming languages .

A   numbering  system  is  a  system  followed  to define a  set of  values  used  to  measure  a  quantity  .  With  the help of numbering  system , we  can express  the  quantitative   dimension  of  any  object  . For example , to express weight  75 kg , Age as 26 Years , Distance as 100 KM and so on.

Number System

However , due to internal design architecture of computer system , this commonly used numerical number system is not suitable and cannot be implemented for the functioning of computer system .

Types Of Number System

A number system is defined as a system that allows to represent any number using a set of combination of symbols , digits and alphabets . The CPU of the computer system can interpret and execute only machine code instructions in Binary . 

And therefore , all program code in any language must be converted to machine code in binary with the help of compiler . However , most programming languages support these four number system while writing a program code.

Types Of Number Systems

Binary Number System

A Binary number system makes use of  only two digits that is 0 and 1. In Binary Number system any number is represented by using only two digits that is 0 and 1 .The  binary number system has base of 2, because it has only two digits to represent any number.

Octal Number System

The Octal number system makes use of  only eight ( 8 ) digits from 0 to 7 to represent any number. In Octal number system any number ( value ) can be represented with combination of any 8 digits ( 0,1,2,3,4,5,6, 7 ). The octal number system has a base of  8, because it has only 8 digits to represent any number

Decimal Number System

The Decimal number system is the most commonly used number system which makes use of ten ( 10 ) digits from 0 to 9 to represent any number. In decimal system any number can be represented with the combination of  10 digits ( 0,1,2,3,4,5,6, 7,8 , 9 ). The decimal number system has a base of 10, because it has  10 digits to represent any number

Hexadecimal Number System

The Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F to represent any number. The Hexadecimal number system makes use of  nine ( 10 ) digits ( 0,1,2,3,4,5,6,7,8,9 )and seven ( 6 ) alphabets ( A,B,C,D,E,F ) to represent any number in this number system. The hexadecimal number system has a base of 16, because it makes use of 16 alphanumeric values.

Number System Types

Binary Number System

In  mathematics  and  digital electronics , a binary number is a number expressed using  binary numeral notation system or base – 2 numeral system . The binary number system  represents any numeric values by  using combination of  only  two  possible  values  that is   0 ( zero )   and    1 ( one ) . In digital electronics this  is  best  suited  to  represent  two   states  ON   or  OFF .

The  Binary number system uses only two digits to represent any number  . Because of its straightforward implementation in digital electronic circuitry using logic gates , the binary system is used  internally by almost all modern  computers  and   computer-based  devices .

 

And therefore  , computer system  is  a  digital  electronic device  which can understand and execute program instructions communicated in terms of two   states  ON   or  OFF  . These two states can be best represented using binary number system.

 

Binary System

Why Computer Use Binary Number System

The computers were invented due to their high computing ability . The computers are used to process large volumes of data at lightning speed . The computer system consist of number of components . Each of these component perform a specific task . One of the most important component in a computer system  is CPU.

The CPU ( Central Processing Unit ) within a computer system is responsible to perform all the arithmetic calculations and logical decisions. The CPU is also referred as microprocessor Or processor chip Or processor.

The processor chip consist of  millions of tiny electronic component called Transistor . The transistor is a fundamental building block for all digital electronic gadgets including computers.

Why Computer Use Binary Number System

The transistor is made-up of silicon which is a semiconductor material . The transistors are used as a micro switch that can be either switched on or switched off . The computer’s  processor , which is the brain of the computer system consist of millions of these transistors . And hence computer processor can understand and execute instructions communicated in the form of only two states that is switch on Or off.  

And therefore , to communicate with computer system , we need a number system that is capable of representing any number using only two digits . The binary number system perfectly fits in to this condition because in binary number system we make use of only two digits that is 0 and 1.

In Binary , the switched ON state is represented 1 ( one ) and the switched OFF state is represented by 0 ( zero ) . And for this reason computer architecture supports binary number system and all computer programs must be first compiled into machine code instructions in binary which computer CPU can execute.

How Data Represented In Binary

The Computer stores all information and program data only in binary digital form. That means all the data be it text, photographs, audio , video or whatever else is comprised of  only  collections   of  ones  and   zeroes. However , the operating system presents this data in a graphical format in GUI environment which we are all familiar .

Data For Computer User
Data For Computer System

Binary Code And Binary Units

Since the computer CPU can execute only machine code instructions and operate on the data in binary , All the  program  code  and  the data must be  represented  in the binary form . The CPU operates  on the data  and  the  result  of  this operation can be  sent  to either output device ( monitor , printer  etc )  or  it  can be stored  in  a  permanent  storage  device for future use.

The  fundamental  building block of digital information is the binary digit or bit, which represents a single 0 ( zero )  or 1 ( one ) state. This is represented by a bit in computer memory  which is the smallest memory unit.

To represent a large amount of  data , the bits can be organized into groups of four , eight , sixteen , 32  or  64 bits , called  nybbles / nibble , bytes , words, long words and very long words  respectively. These are  referred  as  binary  units  of  measurement .

Binary And Computer System Memory

The  computers recognize only two discrete states : on and  off. These states can be represented by two digits ,  0  and 1 .  Each 0 or 1 is called a bit in the binary system. A  Bit is the  smallest unit of data a computer can process. A  Bit is a short for binary digit. The binary system has a base of 2 with the two digits ( 0 and 1 ). By using combinations of 0s and 1s we  can  represent larger numbers.

Binary Number And Logic Gates

The  computer system performs different jobs by   executing  the program  instructions as per the program logic  . The CPU  is  the  main   component  inside a computer system  which performs all arithmetic  calculations  and  also   logical  operations  .

The Computer CPU is responsible to perform both arithmetic calculation and logical operations. The  CPU  is  made-up of  millions  of tiny circuits  called  transistors  which can function as micro switch . The logic gates are  constructed by using transistors  inside  a  processor chip   mainly  used   by   the CPU   to  perform   logical operations  .

The computers are digital machines and logic gates are the basic components in digital electronics. The Logic gates  are used to create digital circuits and even complex integrated circuits. The computer CPU consist of millions these tiny circuits which enable CPU to perform logical operations.     

Logic Gates
Logical Operations By Logic Gates

The processor works by reacting to an input of 0s and 1s in specific manner  and then returning an output based on the  decision. The decision itself happens in a circuit called a logic gate, each of which requires at least one transistor, with the inputs and outputs arranged differently  for  different operations.

Binary Number And Boolean Algebra

In mathematics and mathematical logic , Boolean algebra is the branch of algebra in which the values of the variables are the truth values (  true and false )  and this is usually  denoted  in  binary   1  and  0  respectively.

The Boolean algebra was introduced by George Boole in 1854  who was a British  Mathematician .Boolean algebra has been  fundamental in the development of digital electronics .In algebra we make use of decimal numbers , whereas the boolean algebra uses  truth values , true ( 1 ) and false ( 0 ).

Boolean Algebra

A logic gate is a tiny circuit  used in processors for making a logical decision which  is based on boolean algebra . Boolean Algebra is used to analyze and simplify the digital ( logic ) circuits. It uses only the binary numbers i.e. 0 and 1. It  is  also called  as Binary Algebra  or  Logical Algebra.

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