The phenomenon of the interaction of electric currents or fields and magnetic fields.

the branch of physics concerned with electromagnetism.


Uses of Electromagnetism in Life


Whatever powered devices we use, from table clocks to microwave ovens, have some form of electromagnetic principle involved in their functioning. It is electromagnetism which has given the flexibility for switching of/on electricity as required.

Electromagnets are created by having an iron core wound with a conductor carrying current. The strength of the electromagnet depends upon the amount of current passing through the conductor. Also the current can be easily stopped and started to form an electromagnet and de-energize respectively as per the need of the work to be performed. This is the principle used for moving heavy objects in the scrap yard. Electricity is connected to the circuit to power the electromagnets when they are energized. Thus the magnets start to attract scrap metal (junk cars), and carry them to the designated area. After locating them in a particular location, the electricity is disconnected from the circuit, thus de-energizing the electromagnet, making the scrap metal detach from the magnet.

Uses in Home Appliances:


Many of our electrical home appliances use electromagnetism as a basic principle of working. If we take an example of an electric fan, the motor works on the principle of electromagnetic induction, which keeps it rotating on and on and thus making the blade hub of the fan to rotate,

blowing air. Not restricting to fan, many other appliances use electromagnetism as a basic principle. Electric door bell works on this principle too. When the door bell button is put on, the coil gets energized, and due to the electromagnetic forces, the bell sounds. The working of an electric bell is discussed in detailed manner in one of our articles. The loudspeaker which we use for public announcements in meetings, or to transmit message over a long distance, is a perfect example for an electromagnetic appliance. The movement of the coil under the electromagnetic force produces sound which is heard over a very long distance.

Tape recorder

An audio tape recordertape deck or tape machine is an audio storage device that records and plays back

appliances use electromagnetism as a basic principle. Electric door bell works on this principle too. When the door bell button is put on, the coil gets energized, and due to the electromagnetic forces, the bell sounds. The working of an electric bell is discussed in detailed manner in one of our articles. The loudspeaker which we use for public announcements in meetings, or to transmit message over a long distance, is a perfect example for an electromagnetic appliance. The movement of the coil under the electromagnetic force produces sound which is heard over a very long distance.

Tape recorder

An audio tape recordertape deck or tape machine is an audio storage device that records and plays back sounds, including articulated voices, usually using magnetic tape, either wound on a reel or in acassette, for storage. In its present day form, it records a fluctuating signal by moving the tape across a tape head that polarizes the magnetic domains in the tape in proportion to the audio signal. Tape-recording devices include reel-to-reel tape deck and the cassette deck.

The use of magnetic tape for sound recording originated around 1930. Magnetizable tape revolutionized both the radio broadcast and music recording industries. It gave artists and producers the power to record and re-record audio with minimal loss in quality as well as edit and rearrange recordings with ease. The alternative recording technologies of the era, transcription discs and wire recorders, could not provide anywhere near this level of quality and functionality. Since some early refinements improved the fidelity of the reproduced sound, magnetic tape has been the highest quality analog sound recording medium available. However, as of the first decade of the 21st century, analog magnetic tape is largely being replaced by digital recording technologies for most sound recording purposes.

Prior to the development of magnetic tape, magnetic wire recorders had successfully demonstrated the concept of magnetic recording, but they never offered audio quality comparable to the other recording and broadcast standards of the time. Some individuals and organizations developed innovative uses for magnetic wire recorders while others investigated variations of the technology. One particularly important variation was the application of an oxide powder to a long strip of paper. This German invention was the start of a long string of innovations that have led to present day magnetic tape recordings.


Uses of sensors in Robotics

The sensors are one of the useful technologies, which play a vital role in the robotics field. There are four important categories where uses of sensors are highly required in robotics such as:

  • Safety monitoring
  • Interlocking in work cell control
  • Quality control in work part inspection
  • Data collection of objects in the robot work cell

Safety monitoring:

The sensors are extremely used in industrial robotics for monitoring the hazardous and safety conditions in the robot cell layout. This certainly helps in avoiding the physical injuries and other damages caused to the human workers.

Interlocking in work cell control:

In robot work cell, the series of activities of different equipments are controlled by using interlocks. Here, sensors are employed for verifying the conclusion of the current work cycle before progressing to the next cycle.

Quality control in work part inspection:

In olden days, the quality control was performed with a manual inspection system. Nowadays, sensors are employed in the inspection process for determining the quality features of a work part automatically. A major


The sensors are extremely used in industrial robotics for monitoring the hazardous and safety conditions in the robot cell layout. This certainly helps in avoiding the physical injuries and other damages caused to the human workers.

Interlocking in work cell control:

In robot work cell, the series of activities of different equipments are controlled by using interlocks. Here, sensors are employed for verifying the conclusion of the current work cycle before progressing to the next cycle.

Quality control in work part inspection:

In olden days, the quality control was performed with a manual inspection system. Nowadays, sensors are employed in the inspection process for determining the quality features of a work part automatically. A major advantage of using sensors in this category provides high accurate results. One disadvantage in this automatic inspection is that the sensors are only able to examine a limited variety of work part features and faults.

Data collection of objects in the robot work cell:

Sensors are used in this category to determine the position or other related data about the fixtures, work parts, equipment, human workers, and so on. Apart from sensing the position, it is also implemented to find out the other information like work part’s color, orientation, size, shape, etc. The key reasons for determining the above information while executing a robot program includes:

  • Recognition of work parts
  • Random position and orientation of work parts
  • Improved accuracy of robot position using the feedback data



How do speakers work?

Speakers come in all shapes and sizes, enabling you to listen to music on your iPod, enjoy a film at the cinema or hear a friend’s voice over the phone.

In order to translate an electrical signal into an audible sound, speakers contain an electromagnet: a metal coil which creates a magnetic field when an electric current flows through it. This coil behaves much like a normal (permanent) magnet, with one particularly handy property: reversing the direction of the current in the coil flips the poles of the magnet.

Inside a speaker, an electromagnet is placed in front of a permanent magnet. The permanent magnet is fixed firmly into position whereas the electromagnet is mobile. As pulses of electricity pass through the coil of the electromagnet, the direction of its magnetic field is rapidly changed. This means that it is in turn attracted to and repelled from the permanent magnet, vibrating back and forth.The electromagnet is attached to a cone made of a flexible material such as paper or plastic which amplifies these vibrations, pumping sound waves into the surrounding air and towards your ears.


How cellphones work

the surrounding air and towards your ears.

How cellphones work


Walking and talking, working on the train, always in contact, never out of touch—cellphones have dramatically changed the way we live and work. No one knows exactly how many little plastic handsets there are in the world, but the best guess is over 4.6 billion. That’s around two thirds of the planet’s population! In developing countries, where large-scale land line networks (ordinary telephones wired to the wall) are few and far between, over 90 percent of the phones in use are cellphones. Cellphones (also known as cellular phones and, chiefly in Europe, as mobile phones or mobiles) are radio telephones that route their calls through a network of masts linked to the main public telephone network. Here’s how they work.

Photo: A typical Nokia cellular phone. Back in the 1990s, cellphones like this were merely used for making voice calls. Now networks are faster and capable of handling greater volumes of traffic, cellphones are increasingly used as portable communication centers, capable of doing all the things you can do with a telephone, digital camera, MP3 player, and laptop computer.


How Hard Disks Work


Nearly every desktop computer and server in use today contains one or more hard-disk drives. Everymainframe and supercomputer is normally connected to hundreds of them. You can even find VCR-type devices and camcorders that use hard disks instead of tape. These billions of hard disks do one thing well — they store changing digital information in a relatively permanent form. They give computers the ability to remember things when the power goes out.

In this article, we’ll take apart a hard disk so that you can see what’s inside, and also discuss how they organize the gigabytes of information they hold in files!



Output device

An output device is any piece of computer hardware equipment used to communicate the results of data processing carried out by an information processing system (such as acomputer) which converts the electronically generated information into human-readable form.

Display devices

A display device is an output device that visually conveys text, graphics, and video information. Information shown on a display device is called soft copy because the information exists electronically and is displayed for a temporary period of time. Display devices include CRT monitors, LCD monitors and displays, gas plasma monitors, and televisions.[3]


Inputs are the signals or data received by the system, and outputs are the signals or data sent from it.

There are many input and output devices such as multifunction printers and computer-based navigation systems that are used for specialised or unique applications.[1] In computing, input/output refers to the communication between an information processing system(such as a computer), and the outside world. Inputs are the signals or data received by the system, and outputs are the signals or data sent from it.


Types of output

Some types of output are text, graphics, tactile,[4] audio, and video. Text consists of characters (letters, numbers, punctuation marks, or any other symbol requiring one byte of computer storage space) that are used to create words, sentences, and paragraphs. Graphics are digital representations of nontext information such as drawings, charts, photographs, and animation (a series of still images in rapid sequence that gives the illusion of motion). Tactile output such as raised line drawings may be useful for some individuals who are blind. Audio is music, speech, or any other sound. Video consists of images played back at speeds to provide the appearance of full motion.[3]

Graphics (Visual)


Graphical output displayed on ascreen.

A digital image is a numeric representation of an image stored on a computer. They don’t have any physical size until they are displayed on a screen or printed on paper. Until that point, they are just a collection of numbers on the computer’s hard drive that describe the individual elements of a picture and how they are arranged.[5] Some computers come with built-in graphics capability. Others need a device, called a graphics card or graphics adapter board, that has to be added.[6] Unless a computer has graphics capability built into the motherboard, that translation takes place on the graphics card.[7] Depending on whether the image resolution is fixed, it may be of vectoror raster type. Without qualifications, the term “digital image” usually refers to raster images also called bitmap images. Raster images that are composed of pixels and is suited for photo-realistic images. Vector images which are composed of lines and co-ordinates rather than dots and is more suited to line art, graphs or fonts.[5] To make a 3-D image, the graphics card first creates a wire frame out of straight lines. Then, it rasterizes the image (fills in the remaining pixels). It also adds lighting, texture and color.[7]


Haptic technology, or haptics, is a tactile feedback technology which takes advantage of the sense of touch by applying forces, vibrations, or motions to the user.[8] Severalprinters and wax jet printers have the capability of producing raised line drawings. There are also handheld devices that use an array of vibrating pins to present a tactile outline of the characters or text under the viewing window of the device.[4]


Speech output systems can be used to read screen text to computer users. Special software programs called screen readers attempt to identify and interpret what is being displayed on the screen[9] and speech synthesizers convert data to vocalized sounds or text.[6]


These examples of output devices also include input/output devices.[10][11] Printers and visual displays are the most common type of output device for interfacing to people, but voice is becoming increasingly available.[12]

10 Steps to Creating a WordPress Blog

1.)  Layout: Draw up a layout of how you would like your site to look. Brainstorm the major categories you are going to cover. Research other blogs that you enjoy reading to help you get a feel for how you want your site to look. One big decision is whether you want to have more than one navigation bar.


  • Tim Ferriss’s site Four Hour Blog covers a wide array of topics, way too many to fit across his primary navigation bar. He uses his primary navbar to cover the basics and then a site wide sidebar to cover the topics he frequently writes about.

  •  This navigation bar was taken from a successful affiliate site. They are using their targeted keywords across the navigation bar to maximize the link juice passed across each page. From an SEO perspective, their can be a benefit to limiting the links you have on your navigation bar and each page in general. This sites news section uses a sidebar but it is not used site wide.

2.) Choose a theme:  Many themes are available for free and some great ones are out there for purchase. If I had one piece of advice for choosing a theme it would be to keep it clean. You don’t need a million widgets, images or menu bars on your pages. If you are providing educational or entertaining information that is what the readers will be there for. If you are researching other WordPress blogs while planning your design then at the bottom you can often see what theme they are using.

  • If you just want to use one of the many free ones available then in your WordPress dashboard go: Appearance —> Themes —> Install Themes —> Search

Search for your WordPress theme

3.) Get a Logo/Header: One of the things I love the most about WordPress is outside of a theme, a logo is the only thing you have to spend extra time or money on. Unless you are great with photoshop, I recommend hiring someone from ELance or a forum to design a logo for you. I know I have gotten really nicelogos for as little as $20.00. Make sure you get the pixel specifications from your theme correct and that the logo will mesh with your sites theme and color scheme. Also tell your designer that you want at least one edit as part of the agreement.

4.) Set your permalinks structure: I’ve seen some debate on what the best permalink structure is but you definitely don’t want to leave it on the default. Below is my recommendation but feel free to do some more research.

  • In your dashboard go to Settings->PermalinksChange the URL to a custom structure, and use /%category/%postname%/ as this will allow for SEO friendly URLs like yoursite.com/SEO/links/ as opposed to: yoursite.com/?p=001.
  • Change the Category Base to ./ then click save.  Once you do that, only the . will remain there.  If you leave it as is, your SEO category URL will be yoursite.com/seo/links/ when you want it to be yoursite.com/seo/

5.) Create your primary pages: Now that you’ve set your permalinks it’s time to decide on what will be included in your primary navigation bar and any site wide sidebars. This is a good time to breakout the Google keyword tool and run through some searches on what topics you will be covering the most. Test your assumptions and try to come up with at least five primary keywords for each category. Create these pages (even if you don’t have all your content ready) and organize your navigation bar. On your blog you might want a secondary navigation bar that expands on the topics you will write posts on.

I always recommend creating the following pages which are considered fundamental on a legal and ethical level:

  • Privacy Policy: A privacy policy is where you disclose if you have cookies on your site, what your doing with e-mail you collect and more. Here is a free template but I recommend doing more research specific to your site.
  • Terms & Conditions: This describes how users are allowed to use your website. These vary based on what you include on your site (software, free downloads, etc.) so research what other people in your industry, topic are using.
  • About/Contact: It builds user trust to know who runs the site and if they have a way to get in touch with them. This doesn’t need to be long just a short bio and an e-mail or contact form will suffice.
  • Disclosure: The FTC requires bloggers to disclose if they are getting paid or compensated in anyway for the content on their blog. Many use a disclosure page to go over what content is and is not sponsored or affiliate related.

6.) Set your home page: The WordPress default is to show your latest posts on the front page. If you’d like to have any kind of landing page for home and a blog section than do the following.

Set your WordPress homepage

  • Settings – > Reading: Choose a static page then select your desired home page from the drop down menu. Right below it you can select the page where you would like your blog posts to show up.

7.) Set your navigation menus and widgets: Now that you’ve created your pages you need them to show up on the page where you want. This is very specific to the theme you choose so I don’t want to show visuals that could end up being contradictory. That being said, the general steps are:

  • Dashboard —> Appearance —> Menus – From there you can add pages to your top navigation bar and put them in the order you want.
  • Dashboard —> Appearance —> Widgets – This is generally where you would build your sidebars. You can have more than one sidebar on a page and you can customize what pages they will show up on. As I mentioned previously many sites only have a side bar on their blog page.

8.) Plugin’s: WordPress has a huge variety of  plugins available to help you improve site functionality, SEO, collect e-mails and thousands of other things. The plugins I am recommending here are all free and can be found by going to Plugins —> Add New and searching for the name.

Find your optimal plugins

  • XML Sitemap Generator – Generates an XML Sitemap for better indexing of your site by the SERPS. This also makes it much easier to get your site setup in webmaster tools (Don’t even consider not using this one)
  • SEO Ultimate – Another plug-in you shouldn’t go without even if your theme has solid SEO capabilities. This is the best all around SEO tool for WordPress and its free. You can do everything from changing multiple title tags to editing your meta tag descriptions and adding pages to your robot.txt file.
  • W3 Total Cache and W3 Super Cache – These can majorly improve your sites loading speed and greatly lower the risk of your site crashing from too much traffic.
  • Broken Link Checker – Will notify you of broken links on your site.
  • Permalink Trailing Slash Fixer – If you used my recommended permalinks structure this will add a trailing slash in the URLs if its missing.

9.) Google Analytics: For those that don’t know, Google Analytics (or any other analytics service you might use) allows you to see how many visitors come to your site, what pages they visit, how long they stay and much much more. You may want to do add your analytics code earlier in the process but if you have a theme or plugin that can post your analytics code site wide then it’s fine to wait until the rest of your site structure is setup. To register your site go to Google Analytics and they will walk you through the process.

10.) Webmaster Tools: Submit your site to Google and Bing Webmaster tools (which now covers Yahoo). They have solid instructions in both Bing and Google so I won’t explain this step by step. Depending on the XML sitemap plugin you choose the instructions will also vary slightly. My only other point would be to do this as soon as your site structure is setup if you want the SERP’s to start indexing your pages. I once forgot to do this for two months and couldn’t figure out why a lot of my pages and links weren’t showing up. The data you get from using these tools is also crucial.

Now you have your site setup. It’s getting crawled by the search engines and feeding you data. The hard part comes next, you’ve gotta start posting! Blogging can be very competitive but if you have something interesting to say and you stick with it then good things will happen.



A touch screen is a computer display screen that is also an input device. The screens are sensitive to pressure; a user interacts with the computer by touching pictures or words on the screen.

History of Touch Screen Technology


Historians consider the first touch screen to be a capacitive touch screen invented by E.A. Johnson at the Royal Radar Establishment, Malvern, UK, around 1965 – 1967. The inventor published a full

description of touch screen technology for air traffic control in an article published in 1968.


  • Resistive:A resistive touch screen panel is coated with a thin metallic electrically conductive and resistive layer that causes a change in the electrical current which is registered as a touch event and sent to the controller for processing. Resistive touch screen panels are generally more affordable but offer only 75% clarity and the layer can be damaged by sharp objects. Resistive touch screen panels are not affected by outside elements such as dust or water.
  • Surface wave:Surface wave technology uses ultrasonic waves that pass over the touch screen panel. When the panel is touched, a portion of the wave is absorbed. This change in the ultrasonic waves registers the position of the touch event and sends this information to the controller for processing. Surface wave touch screen panels are the most advanced of the three types, but they can be damaged by outside elements.

Capacitive: A capacitive touch screen panel is coated with a material that stores

  • electrical charges. When the panel is touched, a small amount of charge is drawn to the point of contact. Circuits located at each corner of the panel measure the charge and send the information to the controller for processing. Capacitive touch screen panels must be touched with a finger unlike resistive and surface wave panels that can use fingers and stylus. Capacitive touch screens are not affected by outside elements and have high clarity.




  • -Touchscreen devices have limited buttons that will possibly break after 3 – 4 years
  • -Touchscreen devices usually have more simple user interfaces Ex. Ipod Apps
  • -Having less or not buttons means that you can put more effort into having a big screen 
  • For the people worried about hygiene, most devices are easy to clean, some are even dirt, dust and grease resistant
  • -For people new or uncomfortable with normal desktops, touchscreens are easy to use helping more people get used to using computers



  • -The screen has to be big enough to be able to touch the buttons without missing
  • -Having a big bright screen and needing massive computing power to run this means a very low battery life
  • -In direct sunlight it is much less effictian and most of the time very difficult to read the screen
  • -If a touchscreen devise were to crash the whole screen would be unresponsive, and because of the lack of buttons revoering it would be very difficult
  • -The screens will get very dirty
  • -You have to be within arms reach of the device
  • -They usually cost more than ordinary divices




The Five Generations of Computers

The history of computer development is often referred to in reference to the different generations of computing devices. Each generation of computer is characterized by a major technological development that fundamentally changed the way computers operate, resulting in increasingly smaller, cheaper, more powerful, more efficient and reliable devices.

First Generation (1940-1956) Vacuum Tubes

The first computers used vacuum tubes for circuitry and magnetic drums for memory, and were often enormous, taking up entire rooms. They were very expensive to operate and in addition to using a great deal of electricity, generated a lot of heat, which was often the cause of malfunctions.

First generation computers relied on machine language, the lowest-level programming language understood by computers, to perform operations, and they could only solve one problem at a time. Input was based on punched cards and paper tape, and output was displayed on printouts.

The UNIVAC and ENIAC computers are examples of first-generation computing devices. The UNIVAC was the first commercial computer delivered to a business client, the U.S. Census Bureau in 1951.

vacuum tube


  • Vacuum tubes were the only electronic component available during those days.
  • Vacuum tube technology made possible to make electronic digital computers.
  • These computers could calculate data in millisecond.


  • The computers were very large in size.
  • They consumed a large amount of energy.
  • They heated very soon due to thousands of vacuum tubes.
  • They were not very reliable.
  • Air conditioning was required.

Constant maintenance was required

  • Non-portable.
  • Costly commercial production.
  • Limited commercial use.
  • Very slow speed.
  • Limited programming capabilities.
  • Used machine language only.
  • Used magnetic drums which provide very less data storage.
  • Used punch cards for input.
  • Not versatile and very faulty.

Second Generation (1956-1963) Transistors
Transistors replaced vacuum tubes and ushered in the second generation of computers. The transistor was invented in 1947 but did not see widespread use in computers until the late 1950s. The transistor was far superior to the vacuum tube, allowing computers to become smaller, faster, cheaper, more energy-

efficient and more reliable than their first-generation predecessors. Though the transistor still generated a great deal of heat that subjected the computer to damage, it was a vast improvement over the vacuum tube. Second-generation computers still relied on punched cards for input and printouts for output.


  • Smaller in size as compared to the first generation computers.
  • The 2nd generation Computers were more reliable
  • Used less energy and were not heated.
  • Wider commercial use
  • Better portability as compared to the first generation computers.
  • Better speed and could calculate data in microseconds
  • Used faster peripherals like tape drives, magnetic disks, printer etc.
  • Used Assembly language instead of Machine language.
  • Accuracy improved.


  • Cooling system was required
  • Constant maintenance was required
  • Commercial production was difficult
  • Only used for specific purposes
  • Costly and not versatile
  • Puch cards were used for input.

Third Generation (1964-1971) Integrated Circuits
The development of the integrated circuit was the hallmark of the third generation of computers. Transistors were miniaturized and placed on silicon chips, called semiconductors, which drastically increased the speed and efficiency of computers.



  • Smaller in size as compared to previous generations.
  • More reliable.
  • Used less energy
  • Produced less heat as compared to the previous two generations of computers.
  • Better speed and could calculate data in nanoseconds.
  • Used fan for heat discharge to prevent damage.
  • Maintenance cost was low because hardware failure is reared.
  • Totally general purpose
  • Could be used for high-level languages.
  • Good storage
  • Versatile to an extent
  • Less expensive
  • Better accuracy
  • Commercial production increased.
  • Used mouse and keyboard for input.


  • Air conditioning was required.

Highly sophisticated technology required for the manufacturing of IC chips.
Fourth Generation (1971-Present) Microprocessors

the microprocessor brought the fourth generation of computers, as thousands of integrated circuits were built onto a single silicon chip. What in the first generation filled an entire room could now fit in the palm of the hand. The Intel 4004 chip, developed in 1971, located all the components of the computer—from the central processing unit and memory to input/output controls—on a single chip.

In 1981 IBM introduced its first computer for the home user, and in 1984 Apple introduced the Macintosh. Microprocessors also moved out of the realm of desktop computers and into many areas of life as more and more everyday products began to use microprocessors.

As these small computers became more powerful, they could be linked together to form networks, which eventually led to the development of the Internet. Fourth generation computers also saw the development of GUIs, the mouse and handheld devices.



  • More powerful and reliable than previous generations.
  • Small in size
  • Fast processing power with less power consumption
  • Fan for heat discharging and thus to keep cold.
  • No air conditioning required.
  • Totally general purpose
  • Commercial production
  • Less need of repair.
  • Cheapest among all generations
  • All types of High level languages can be used in this type of computers


  • The latest technology is required for manufacturing of Microprocessors.

    Fifth Generation (Present and Beyond) Artificial Intelligence

    Fifth generation computing devices, based on artificial intelligence, are still in development.

Though there are some applications, such as voice recognition, that are being used today. The use of parallel processing and superconductors is helping to make artificial intelligence a reality. Quantum computation and molecular and nanotechnology will radically change the face of computers in years to come. The goal of fifth-generation computing is to develop devices that respond to natural language input and are capable of learning and self-organization.

Scientists are working hard on the 5th generation computers with quite a few breakthroughs. It is based on the technique of Artificial Intelligence (AI). Computers can understand spoken words & imitate human reasoning. Can respond to its surround dings using different types of sensors. Scientists are constantly working to increase the processing power of computers. They are trying to create a computer with real IQ with the help of advanced programming and technologies. IBM Watson  computers one example that outsmarts Harvard University Students. The advancement in modern technologies will revolutionize the computer in future.

Binary to Decimal Conversion

How to Convert Binary to Decimal

Conversion of binary to decimal (base-2 to base-10) numbers and back is an important concept to understand as the binary numbering system forms the basis for all computer and digital systems. The decimal or “denary” counting system uses the Base-of-10 numbering system where each digit in a number takes on one of ten possible values, called “digits”, from 0 to 9, eg. 21310 (Two Hundred and Thirteen).

But as well as having 10 digits ( 0 through 9 ), the decimal numbering system also has the operations of addition ( + ), subtraction ( ), multiplication ( × ) and division ( ÷ ).

In a decimal system each digit has a value ten times greater than its previous number and this decimal numbering system uses a set of symbols, b, together with a base, q, to determine the weight of each digit within a number. For example, the six in sixty has a lower weighting than the six in six hundred. Then in a binary numbering system we need some way of converting Decimal to Binary as well as back from Binary to Decimal.

Any numbering system can be summarised by the following relationship:

N = bi qi
where: N is a real positive number
b is the digit
q is the base value
and integer (i) can be positive, negative or zero

N = bn qn… b3 q3 + b2 q2 + b1 q1 + b0 q0 + b-1 q-1 + b-2 q-2… etc.

The Decimal Numbering System

In the decimal, base-10 (den) or denary numbering system, each integer number column has values of units, tens, hundreds, thousands, etc as we move along the number from right to left. Mathematically these values are written as 100, 101, 102, 103 etc. Then each position to the left of the decimal point indicates an increased positive power of 10. Likewise, for fractional numbers the weight of the number becomes more negative as we move from left to right, 10-1, 10-2, 10-3 etc.

So we can see that the “decimal numbering system” has a base of 10 or modulo-10 (sometimes called MOD-10) with the position of each digit in the decimal system indicating the magnitude or weight of that digit as q is equal to “10” (0 through 9). For example, 20 (twenty) is the same as saying 2 x 101 and therefore 400 (four hundred) is the same as saying 4 x 102.

The value of any decimal number will be equal to the sum of its digits multiplied by their respective weights. For example:  N = 616310 (Six Thousand One Hundred and Sixty Three)  in a decimal format is equal to:

6000 + 100 + 60 + 3 = 6163

or it can be written reflecting the weight of each digit as:

( 6×1000 ) + ( 1×100 ) + ( 6×10 ) + ( 3×1 ) = 6163

or it can be written in polynomial form as:

( 6×103 ) + ( 1×102 ) + ( 6×101 ) + ( 3×100 ) = 6163

Where in this decimal numbering system example, the left most digit is the most significant digit, or MSD, and the right most digit is the least significant digit or LSD. In other words, the digit 6 is the MSD since its left most position carries the most weight, and the number 3 is the LSD as its right most position carries the least weight.

The Binary Numbering System

The Binary Numbering System is the most fundamental numbering system in all digital and computer based systems and binary numbers follow the same set of rules as the decimal numbering system. But unlike the decimal system which uses powers of ten, the binary numbering system works on powers of two giving a binary to decimal conversion from base-2 to base-10.

Digital logic and computer systems use just two values or states to represent a condition, a logic level “1” or a logic level “0”, and each “0” and “1” is considered to be a single digit in a Base-of-2 (bi) or “binary numbering system”.

In the binary numbering system, a binary number such as 101100101 is expressed with a string of “1’s” and “0’s” with each digit along the string from right to left having a value twice that of the previous digit. But as it is a binary digit it can only have a value of either “1” or “0” therefore, q is equal to “2” (0 or 1) with its position indicating its weight within the string.

As the decimal number is a weighted number, converting from decimal to binary (base 10 to base 2) will also produce a weighted binary number with the right-hand most bit being the Least Significant Bit or LSB, and the left-hand most bit being the Most Significant Bit or MSB, and we can represent this as:

Representation of a Binary Number

MSB Binary Digit LSB
28 27 26 25 24 23 22 21 20
256 128 64 32 16 8 4 2 1

We saw above that in the decimal number system, the weight of each digit to the left increases by a factor of 10. In the binary number system, the weight of each digit increases by a factor of  2 as shown. Then the first digit has a weight of  120 ), the second digit has a weight of  221 ), the third a weight of  422 ), the fourth a weight of  823 ) and so on.

So for example, converting a Binary to Decimal number would be:

Decimal Digit Value 256 128 64 32 16 8 4 2 1
Binary Digit Value 1 0 1 1 0 0 1 0 1

By adding together ALL the decimal number values from right to left at the positions that are represented by a “1” gives us:  (256) + (64) + (32) + (4) + (1) = 35710 or three hundred and fifty seven as a decimal number.

Then, we can convert binary to decimal by finding the decimal equivalent of the binary array of digits 1011001012 and expanding the binary digits into a series with a base of  2 giving an equivalent of 35710 in decimal or denary.

Repeated Division-by-2 Method

We have seen above how to convert binary to decimal numbers, but how do we convert a decimal number into a binary number. An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero.

So for example.  Convert the decimal number 29410 into its binary number equivalent.

Number 294 Dividing each decimal number by “2” as shown will give a result plus a remainder.

If the decimal number being divided is even then the result will be whole and the remainder will be equal to “0”. If the decimal number is odd then the result will not divide completely and the remainder will be a “1”.

The binary result is obtained by placing all the remainders in order with the least significant bit (LSB) being at the top and the most significant bit (MSB) being at the bottom.

divide by 2
result 147 remainder 0  (LSB)
divide by 2
result 73 remainder 1
divide by 2
result 36 remainder 1
divide by 2
result 18 remainder 0
divide by 2
result 9 remainder 0
divide by 2
result 4 remainder 1
divide by 2
result 2 remainder 0
divide by 2
result 1 remainder 0
divide by 2
result 0 remainder 1  (MSB)

This divide-by-2 decimal to binary conversion technique gives the decimal number 29410 an equivalent of 1001001102 in binary, reading from right to left. This divide-by-2 method will also work for conversion to other number bases.

Then we can see that the main characteristics of a Binary Numbering System is that each “binary digit” or “bit” has a value of either “1” or “0” with each bit having a weight or value double that of its previous bit starting from the lowest or least significant bit (LSB) and this is called the “sum-of-weights” method.

So we can convert a decimal number into a binary number either by using the sum-of-weights method or by using the repeated division-by-2 method, and convert binary to decimal by finding its sum-of-weights.

Binary Number Names & Prefixes

Binary numbers can be added together and subtracted just like decimal numbers with the result being combined into one of several size ranges depending upon the number of bits being used. Binary numbers come in three basic forms – a bit, a byte and a word, where a bit is a single binary digit, a byte is eight binary digits, and a word is 16 binary digits.

The classification of individual bits into larger groups are generally referred to by the following more common names of:

Number of Binary Digits (bits) Common Name
1 Bit
4 Nibble
8 Byte
16 Word
32 Double Word
64 Quad Word

Also, when converting from Binary to Decimal or even from Decimal to Binary, we need to be careful that we do not mix up the two sets of numbers. For example, if we write the digits 10 on the page it could mean the number “ten” if we assume it to be a decimal number, or it could equally be a “1” and a “0” together in binary, which is equal to the number two in the weighted decimal format from above.

One way to overcome this problem when converting binary to decimal numbers and to identify whether the digits or numbers being used are decimal or binary is to write a small number called a “subscript” after the last digit to show the base of the number system being used.

So for example, if we were using a binary number string we would add the subscript “2” to denote a base-2 number so the number would be written as 102. Likewise, if it was a standard decimal number we would add the subscript “10” to denote a base-10 number so the number would be written as 1010.

Today, as micro-controller or microprocessor systems become increasingly larger, the individual binary digits (bits) are now grouped together into 8’s to form a single BYTE with most computer hardware such as hard drives and memory modules commonly indicate their size in Megabytes or even Gigabytes.

Number of Bytes Common Name
1,024 (210) kilobyte (kb)
1,048,576 (220) Megabyte (Mb)
1,073,741,824 (230) Gigabyte (Gb)
a very long number! (240) Terabyte (Tb)

Binary to Decimal Summary

  • A “BIT” is the abbreviated term derived from BInary digiT
  • A Binary system has only two states, Logic “0” and Logic “1” giving a base of 2
  • A Decimal system uses 10 different digits, 0 to 9 giving it a base of 10
  • A Binary number is a weighted number who’s weighted value increases from right to left
  • The weight of a binary digit doubles from right to left
  • A decimal number can be converted to a binary number by using the sum-of-weights method or the repeated division-by-2 method
  • When we convert numbers from binary to decimal, or decimal to binary, subscripts are used to avoid errors

Converting binary to decimal (base-2 to base-10) or decimal to Binary Numbers (base10 to base-2) can be done in a number of different ways as shown above. When converting decimal numbers to binary numbers it is important to remember which is the least significant bit (LSB), and which is the most significant bit (MSB).

In the next tutorial about Binary Logic we will look at converting binary numbers into Hexadecimal Numbers and vice versa and show that binary numbers can be represented by letters as well as numbers.