This Article is About
binary numbers
what this means
Binary Math: How To Convert Binary Numbers
Join 1000's of Authors at StreetArticles Today!


If you are studying for CCNA or Network+ certification, you will have to be able to do Binary and Hexadecimal number conversions without the use of a calculator. This article discusses why we use binary math in comuters, some commonly used terms that are related to binary, and then outlines how to do binary conversions.

Computer Math Terms

Bits, Bytes, Megs, Gigs...... You undoubtedly have heard these terms. Just turn on your television and wait until the next Dell or HP ad comes on. What does it all mean? As humans, we have all adopted the decimal notation system 0 - 9. But, when computers were first created, there needed to be a much simpler way of addition. "Why" you may ask? Computers operate off electricity and the easiest way to communicate with electricity is "on" or "off".


The simplest unit in binary math is called a Bit. The bit can have only one of two values, 1 or 0. A group of 8 bits is called a Byte (I think the creator of binary math must have been hungry.) When written down, the most significant bit is on the left and the least significant bit is on the right. What this means is that number's value increases when you add more places to the left. Take decimal as an example: the first digit can be any number from 0 - 9. When you reach 10, the second digit(most significant) becomes a one and the first digit (least significant) starts again at 0. However, in binary, each bit can only be 0 or 1. So if you want to get to 2 you have to add another bit 10. I know it kind of looks like decimal 10, but it is actually decimal 2. This is why it is important to understand which notation you are in. Decimal 10 is actually 1010 in binary. A neat little trick to remember is that if the last bit is 0, the number is even. If it is 1, the number is odd.

Just like in decimal we have "benchmarks" when we reach larger numbers, so there are in binary. Even though the bit is technically the smallest unit in computing, we usually use the byte as the smallest number. One byte is 8 bits in length. A Kilobyte is 1,000 bytes and a Megabyte is 1,000,000 bytes. Gigabytes are in the Billions. Computers now hold Terabytes or more of information. That's 1 Trillion bytes!

Converting Decimal into Binary

When converting decimal into binary, it is easier if you draw out a chart for the powers of 2 starting from right to left. For example an 8-bit number would look like this:

128    64     32     16      8      4      2      1

Let's say we want to know what 110 would look like in binary. We would first divide 110 into 128 to see if we get 0 or 1 (ignore the remainder). We do not want 2 because in binary, each place can only be either 1 or 0.

110/128 = 0   this is our first bit

then we would subtract 0 from 110 and divide the answer into the next number. in this case 110 - 0 is still 110 so:

110/64 = 1 this is our second bit    subtract 64 from 110 = 46

46/32 = 1     subtract 32 from 46 = 14

14/16 = 0

14/8 = 1    14-8 = 6

6/4 = 1       6-4 = 2

2/2 = 1

Then once you subtract down to zero with no remainder, fill in the rest with zeros. Once you place the ones and zeroes in your chart, you get 01101110.

Converting Binary to Decimal

To go the other way, you would still use the chart, but fill in the binary number underneath. Let's use a binary 11000101 as an example:

128   64    32    16    8     4     2     1 (chart)

  1      1      0      0     0     1     0     1 (plug in the number)

This is the easy part. Only where there is a 1, write down the number above it in the chart. Write them down underneath each other and add them together.




1 +

197 is the decimal equivalent!

IP Addresses

IP addresses are where you will be using these type of conversions most often as a Network Professional. This is because, often it is necessary to segment larger IP addresses into subnets. An IP address is a 32-bit address broken down into four 8-bit octets separated by decimals. Commonly, they are shown in dotted-decimal notation because it's easier for us to think in decimal. This just means it looks like this:

Since each octet has only 8 bits (hence the term octet) there are a total of 256 numbers which can be assigned to the octet 0 - 255 (don't forget, 0 is a value too). Written out as binary, that number would look like this: 11000000101010000000000100000001

Wrap Up

I hope this has been helpful to those of you studying for your Network+ or CCNA exams. Of, course, you would probably use a calculator to do the conversions, however, you will not have a calculator in the exam room with you so you have to feel comfortable doing the conversions on paper or in your head.

Remember that computers only know Binary. Binary numbers are a string of 1s and 0s that correspond electrical signals which have significance to computers. binary is considered a base 2 number system which means that there are only two possible values for each place in a binary number. The most significant bit is written as the left-most bit and the least-significant is on the right.

Remember how to convert binary to decimal and decimal to binary as you will need to do this for the exam without a calculator. IP addresses are 32-bit numbers written in 8-bit octet dotted-decimal notation.

Street Talk

No comments present
You May Also Like
Get A Uk Ip Address In France
For people from France, obtaining an IP address from the UK is something that may be highly desirable. Under normal circumstances, your IP address is a direct indication of where you are living. So if you are in France, your internet service provider will give you an IP address from…
By: Rodders Gillam in  Computers and Technology  >  Software   Oct 06, 2012  
  Likes: 1

New Interconnecting Cisco Networking Devices Part 2 200 - 105 Icnd2 Exam Latest Dumps
Endexam have different 200-105 Interconnecting Cisco Networking Devices Part 2 (ICND2 v3.0) for different candidates. With these Endexam targeted training, the candidates can pass the exam much easier. A lot of people who participate in the IT professional certification exam was to use Endexam Interconnecting Cisco Networking Devices Part 2…
By: aaron14 in  Computers and Technology  >  Certification Tests   Jun 08, 2016  
  Likes: 2

Killtest Offers Huawei Hcie - storage H13 - 629 Practice Questions And Answers For Learning
After you begin to use the H13-629 study materials together with H13-629 real and original exam questions and answers, you should understand the difference. Case for Huawei qualification can apply regarding employment everywhere in the earth. Huawei qualification may be the identity for ensure. An expert could strengthen his/her capacities…
By: Dolton2016 in  Computers and Technology  >  Certification Tests   Jun 08, 2016  
  Likes: 2

Updated Huawei Hcna H31 - 211 - Enu Real Questions
To pass Huawei H31-211-ENU test with great ease and comfort you can prepare this by using Huawei HCNA H31-211-ENU real questions. Huawei HCNA H31-211-ENU real questions are located on countless websites on the Internet but Killtest provides the right practice test and H31-211-ENU exam questions and answers. Killtest is well…
By: Dolton2016 in  Computers and Technology  >  Certification Tests   Jun 06, 2016  
  Likes: 1

Passtcert Cisco 100 - 105 Icnd1 Preparation Material
The training materials of Passtcert website have a unique good quality on the internet. If you want to pass the Cisco 100-105 exam, you'd better to buy Passtcert Cisco 100-105 ICND1 preparation material quickly.Passtcert guarantee exam success rate of 100% ratio, except no one. You choose Passtcert, and select the…
By: connie4 in  Computers and Technology  >  Certification Tests   Jun 06, 2016  
  Likes: 1

Passtcert Microsoft Dynamics CRM Mb2 - 712 Exam Dumps
Passtcert pledge to customers is that we can help customers 100% pass their IT certification exams. The quality of Passtcert Microsoft Dynamics CRM MB2-712 exam dumps has been recognized by many IT experts. The most important characteristic of our products is their pertinence. It only takes 20 hours for you…
By: connie4 in  Computers and Technology  >  Certification Tests   Jun 06, 2016  
  Likes: 0

Latest Cisco Ccna Wireless 200 - 355 PDF Questions
The Cisco CCNA Wireless 200-355 PDF questions of the Endexam is specifically designed for candicates. It is a professional exam materials that the IT elite team specially tailored for you. Passed the exam certification in the IT industry will be reflected in international value. There are many Cisco CCNA Wireless…
By: aaron14 in  Computers and Technology  >  Certification Tests   Jun 04, 2016  
  Likes: 1

H11 - 811 - enu Hcna - uc (unified Communication) Test Questions Guarantee You Success
Killtest H11-811-ENU HCNA-UC (Unified Communication) test questions includes H11-811-ENU study material, Huawei certification H11-811-ENU practice test, H11-811-ENU practice exam, H11-811-ENU free H11-811-ENU demo and much more which will not only enhance your abilities to cope with the problems but you will also be able to manage online real time problems.…
By: Dolton2016 in  Computers and Technology  >  Certification Tests   Jun 04, 2016  
  Likes: 1

It - dumps Cisco 300 - 460 Cldinf Ccnp Cloud Practice Questions
To achieve a specialist or even expert place within Cisco work accreditation, passing 300-460 exam within 300-460 questions and answers are a preceding step. Most of Cisco 300-460 CLDINF CCNP Cloud practice questions will provide you with your hands-on practical knowledge and give by far the most wide-ranging programs about.…
By: Stephen Smith1 in  Computers and Technology  >  Certification Tests   Jun 03, 2016  
  Likes: 1

Ccnp2015 Cisco Ccnp Cloud 300 - 460 Cldinf Exam Dumps
As long as you choose to purchase CCNP2015 cisco CCNP Cloud 300-460 CLDINF exam dumps, we will do our best to help you pass 300-460 exam disposably. In recent years, fierce competition agitates the forwarding IT industry in the world. And IT certification has become a necessity. If you want…
By: connie4 in  Computers and Technology  >  Certification Tests   Jun 03, 2016  
  Likes: 0

IBM C8010 - 725 Websphere Commerce V7 (fep 7) Exam Questions
IBM C8010-725 WebSphere Commerce V7 (FEP 7) exam questions as well as C8010-725 exam engine has become prepared for you actually with the skilled as well as seasoned group of the usb ports professionals who contain a prolonged example of students concerns and needs with the mentioned qualifications. IBM C8010-725…
By: Dolton2016 in  Computers and Technology  >  Certification Tests   Jun 02, 2016  
  Likes: 0

Released Cisco 300 - 460 Cldinf Questions And Answers
Cisco 300-460 is very difficult and passing rate is relatively low. But enrolling in the Cisco certification 300-460 exam is a wise choice, because in today's competitive IT industry, we should constantly upgrade ourselves. However, you can choose many ways to help you pass the exam.The training tools of Endexam…
By: aaron14 in  Computers and Technology  >  Certification Tests   Jun 02, 2016  
  Likes: 0

Endexam Huawei Hcnp H31 - 121 - enu Exam Bootcamp
The curtain of life stage may be opened at any time, the key is that you are willing to show, or choose to avoid. Most of People who can seize the opportunityin front of them are successful. So you have to seize this opportunity of Endexam. Only with it can…
By: aaron14 in  Computers and Technology  >  Certification Tests   Jun 01, 2016  
  Likes: 0

Server2012exam Microsoft Certification 70 - 411 Exam Bootcamp
If you are ready to take the exam, and then use our server2012exam Microsoft certification 70-411 exam bootcamp, we guarantee that you can pass it. If you do not pass the exam, we can give you a refund of the full cost of the materials purchased, or free to send…
By: aaron14 in  Computers and Technology  >  Certification Tests   May 31, 2016  
  Likes: 0

IBM Certified Application Developer C8010 - 725 Study Guide
Killtest IBM Certified Application Developer C8010-725 study guide offer clarifications and additional guidance and address evolving IBM requirements not previ-ously addressed in IBM WebSphere Commerce V7 FEP 7 Application Development. This new version updates the standards to keep pace with emerging threats, technology evolution, and changes in the market. Through…
By: Dolton2016 in  Computers and Technology  >  Certification Tests   May 30, 2016  
  Likes: 1

Article Views: 3030    Report this Article