Adding and Subtracting Hexadecimal

In a previous blog, I talked about hexadecimal and the symbols used to represent numbers in it. Today, I will be explaining how to add and subtract hexadecimal numbers or hex for short. I will be only be dealing with positive numbers as negatives numbers are very complicated in both binary and hexadecimal. Now lets get started!

Adding in hex is very similar to binary. First, you set it up like you are adding base ten numbers in math class. Then, you add the right most digits. If those two digits add up to more than 16, subtract 16 from that number and add one to the digit to the left. Repeat until the number is added out. I have shown an example below:

Add B4 and FO in base 16

B4      (180 in base 10)                                                                                                             +FO     (240 in base 10)                                                                                                                  1A4      (420 in base 10)                 As you can see (B+F is 26. 26-16 is 10 or A)

 

Subtraction in hex is also very similar to subtraction in binary. First you set the equation up like above, but you use a subtraction sign instead of addition. Then you subtract the right-most digits. If the digit being subtracted is larger than the one above, you “borrow” one from the digit to the left which increases the value that you found by 16.

Subtract 1F from 7A in base 16

7A       (122 in base 10)                                                                                                                -1F      (31 in base 10)                                                                                                                     5B       (91 base 10)

 

If you want to check your answers, convert all numbers to base 10 and add or subtract them. If you need more practice, here are some more questions below. Answers are posted under the Youtube video.

  1. Add 8F and F9
  2. Add ABC and 159
  3. Add 123, 456, and 789
  4. Subtract 5D from 8A
  5. Subtract 5DC from 7FA
  6. Subtract ABC and 598 from 1F0D

 

If you are still confused, please watch this Youtube video. Ignore the part where he put 8+B = 13.

  1. 188
  2. C15
  3. D02
  4. 2D
  5. 21E
  6. 4B9

Converting Between Hexadecimal and Binary

As said before in an earlier post, numbers are calculated in different bases. The most used types are base two (also known as binary), base 10 (which we use mainly in mathematics), and hexadecimal, which is what we will be learning about today. As you know, there are no symbols to represent numbers that are 10 or up. So here are the following shortcuts that are used in hexadecimal.

  • For numbers 0-9, use the regular 0-9
  • For the number 10 – use the symbol A
  • For the number 11 – use the symbol B
  • For the number 12 – use the symbol C
  • For the number 13 – use the symbol D
  • For the number 14 – use the symbol E
  • For the number 15 – use the symbol F

For example, numbers can look like 17F, 7B9, ABC, and much much more.

 

So why is hexadecimal used?                                                                                                   Hexadecimal is used as a simplification of binary. For example:

  • In binary, 289 is represented as 0001 0010 0001
  • In hexadecimal, 289 is represented as 121

As you can see, it is much easier to use hexadecimal than to use binary.

 

Now lets talk about the relation between binary and hexadecimal. As you know, each binary digit is known as a bit (0101 has 4 bits).  Eight of these is known as a byte (0100 0111). Lastly, a nibble is four bits (0101), which hexadecimal uses. Converting from binary to hexadecimal, every nibble is one digit in hexadecimal. Here is one example shown:

Convert 1011100 to Hexadecimal:

0101  1100                  First, split the binary number into different nibbles

5         12                      Convert these nibbles into base 10 numbers

5C                                Convert the base 10 numbers to hexadecimal

 

Here are some practice problems. Answers to these are under the Youtube video.

  1. Convert 0010 1010 1010 from binary to hexadecimal
  2. Convert 0010 1011 from binary to hexadecimal
  3. Convert 1010100 from binary to hexadecimal
  4. Convert 111001011 from binary to hexadecimal
  5. Convert 50 base ten to hexadecimal (Convert to binary first)
  6. Convert 829 base ten to hexadecimal

 

If your are still having trouble understanding this, please use this Khan Academy video that explains the concept pretty well.

  1. 2AA
  2. 2B
  3. 54
  4. 1CB
  5. 32
  6. 33D

 

 

History of the internet Pt. 3 – The Modern Day Internet

After the .com crash, many people were a lot more reluctant to invest into some .com websites that they had previously invested in. But then, in 2004, the call to Web 2.0 was suggested and from then on, the internet would grow even faster. Hard drives would gradually replace slower floppy disks, going from megabytes to gigabytes. High speed internet was more affordable and therefore more widespread. Social media platforms like Twitter and Facebook were created.

Then, around 2007-2008, the mobile revolution happened. Now, people could take what was essentially a mini computer everywhere. They could communicate, they could take photos and take videos. People could use mobile data like 4G and WiFi, location-based sources became a lot more common, and many people started using the internet. On mobile, the term app emerged which actually stands for application program or just program. Withthe mobile revolution, the internet grew to the internet that we know today, a fast, reliable platform where you can browse and basically do whatever you want. After this, we would go on to have the internet in space when an astronaut updated his Twitter while in orbit in 2010 and also accomplish some other things. But the internet we know today basically ends around 2010 and the late 2000s.

History of the Internet Part 2 – Moving Towards the Modern Day Internet

In part one of the history of the internet, I talked about what the early internet was like. I covered the ARPANET, the NSFNET, and the evolution towards the modern day internet that most of us know today. Today, I will be covering the remaining of the history of the internet into the 21st century and the modern day internet that everyone knows. After the NSFNET, many people started to recognize the usefulness of the internet and began to start using it. The catch was that in some areas, many people still didn’t use it while in others, many people used it. Also, a lot of people were using a lot of different networks. So, to transition to a more advanced internet, everyone had to move to one very big network or at least a few big networks.

Up until this point, the common citizen didn’t really use the internet. The internet was mainly reserved for government purposes only. But then, ISP’s (Internet Service Providers) started forming. They were mainly formed because people were beginning to understand the usefulness of the internet. Therefore, many people wanted to use the internet for commercial purposes and then, ISP’s were formed. After the Science and Advanced Technology Act was passed by the U.S. Congress, the NSF was allowed to intercommunicate the private research and education networks with the commercial based networks allowing them to research about the same topics and communicate with each other. By the 1900s, the ARPANET was no longer needed as it’s goals had been fulfilled. Also, the NSFNET was no longer the driving factor behind growing the internet. There were many other networks that were also able to carry out the same tasks that the NSFNET could. So on April 30, 1995, the NSF ended its sponsorship to the NSFNET. This meant that there were not really anymore government networks stopping commercial networks. Therefore, the commercial basically had free reign over the internet.

Let’s quickly talk about www. www actually stands for World Wide Web. It is a space where all the URL’s correspond to a website or document. These URL’s are interlinked by hypertext and can be accessed using a web browser or web-based applications. In 1993, Marc Andreessen released the NCSA Mosaic which would trigger a spike in the amount of internet users. This was because the program was easy to use and install, and could be accessed on a home computer. This browser was also one of the earliest browsers that could put text and image on the same page. Then in 1994, Marc Andreessen released Netscape which was an improved version of the NCSA Mosaic. This resulted in one of the earliest browser wars and Marc Andreessen and his Netscape would ultimately lose to the Microsoft Internet Explorer. This resulted in the Windows operating system and the Internet Explorer that we all know and love today.

Let’s move back to the late 1900s. As of right now, the smartphones that almost everyone has now-a-days, almost no one had back then as they were a luxury and only used for business. There was no Social Media like Instagram or Snapchat. Back then, many people still did not have computers in their houses. Computers could not process videos, only DVDs and eventually, CDs. The computer back then was mainly used for eCommerce, email, and forums or bulletin boards. But then, some people started to recognize how much value eCommerce had in it. So people started putting their stock money into eCommerce businesses like Amazon and eBay. These companies were shot to very overpriced valuations and people started selling their stocks which resulted in a market crash known as the .com bubble. This mainly affected companies using the .com level domain.

The History of the Internet Pt. 1

Ever since inventions like the telephone and the telegraph, the internet has begun to evolve. Unlike inventions like the airplane and the light bulb, the internet was created as a group effort and wasn’t really created by one person. Instead, it has evolved over time starting with the NPL Network and the Arpanet. Both of these networks used packet switching. Packet switching is when you send a message, you break the message up into individual parts and then send them all. Then when they get to the destination, they automatically reassemble themselves. Then, they tested the Arpanet. The teams set up labs at UCLA and Stanford and tried to type letters to each other. The receiving team received just two letters before the system crashed, but nevertheless, a new era had begun.

Now, let’s fast forwards a bit. Now, the year is 1973. Although there are many little networks, there isn;t a large a large network encompassing a large enough area to be useful. So now, the little networks had to combine to make one big network. After the Arpanet was up and working, people began to realize that this small networks wasn’t big enough. Then in 1981, the NSF took a liking into the Arpanet network. So the government started giving some of it’s money into the Arpanet. The Arpanet would then eventually be renamed into the NSFNET. The NSFNET first had a network speed of 56kbit/s speed. This was too slow and the system would eventually get overloaded. So the system was upgraded to 1.5Mbit/s. Finally, the NSFNET was upgraded to 45MBit/s. The NSFNET had the ability to connect university and college campus networks to a regional network.

In conclusion, during the mid to late 1900s, many new discoveries were made to contribute to the evolution of technology like the Arpanet and the NSFNET. In the next part, we will progress more to the 21st century and how the internet in the 1990s really evolved into the internet that we know today.