Every now and then it’s nice to take break from tutorials, and look at something a little geekier. We’ve all seen binary code, and most people know it’s made up of two characters, zero and one. Most people also understand that binary code can be converted into decimal by taking the binary number from the right-hand-side of the sequence and applying it to another sequence of numbers “two to the power of”. For example an eight digit binary code could look like this – “10010001”. This includes one “1”, one “16”, and one “128”, making a grand total of 145. That’s fairly simple. It gets more complex when you add more numbers but the principal is the same.

Now – if you do a lot of HTML work, you will have seen codes that represent colors. These codes include letters, and are in hexadecimal. The letters are actually numbers but because the characters we commonly use are in base 10, i.e. the digits 0 through to 9, we have to use letters to represent the numbers 10,11,12,13,14 and 15. This is because hexadecimal is base 16, and has 16 digits including zero. We don’t use two characters in a hexadecimal number until we get to the number 16, which is actually “10”. This represents one sixteen. The hexadecimal number “18” is actually sixteen plus 8, which is 24. The hex code “1F” represents 31 in decimal because we have one sixteen plus 15. Get the idea?

Okay, so we can mostly work out what a hex number in decimal is when we only have two characters. One digit represents how many “16”s we have, and the other is simply counting from zero to fifteen. So the highest number we have is “FF”, which is fifteen times sixteen, plus fifteen. The answer is 255. Already you can see the benefits of hex, because in binary that number would require eight characters, and we’ve done it in two.

So how do we solve bigger numbers into decimal easier? The answer is to split each hex character into its binary equivalent. So the hex number 8FA4 becomes in binary 1000.1111.1011.0100. Here we can see each number that makes up the ultimate answer. Starting from the left we have a 4, a 16, a 32, a 128 etc… all the way up to the last character, which is a 32,768. Add all the numbers represented by ones together and we have 36772. So our hex code of 8FA4 is actually 36772 in decimal. Four characters to represent something that is sixteen characters in binary is very impressive indeed.

If you remember back your hex codes in HTML that represent colors, you’ll notice that you have hex codes of 6 characters. The first character represents 16’s, the second 16’s to the power 2, the third is sixteen to the power 3 and so on. If you work it out, the largest number you can have with six hex digits is 16,777,215. Nearly seventeen million colors represented by only six characters.

AdvertisementAdvertising revenue is falling fast across the Internet, and independently-run sites like Ghacks are hit hardest by it. The advertising model in its current form is coming to an end, and we have to find other ways to continue operating this site.

We are committed to keeping our content free and independent, which means no paywalls, no sponsored posts, no annoying ad formats or subscription fees.

If you like our content, and would like to help, please consider making a contribution:

Previous Post: « Increase your Laptop’s Battery Life with Advanced Power Settings

Next Post: How To Crop Videos With Free Software »

Please click on the following link to open the newsletter signup page: Ghacks Newsletter Sign up

- Chrome Extension Manifest V3 could end uBlock Origin for Chrome
- How to remove DarkMatter Certificates from Firefox
- Microsoft: Don't buy Office 2019
- A look at Firefox's new about:config page
- 2019: the year I dropped all entertainment subscription plans
- Pale Moon 28.4.0 released: security and stability update
- The new Skype for Web does not work in Firefox or Opera
- Windows 7 to show notifications about upcoming support end
- Integrate Nano Defender with uBlock Origin to block Anti-Adblocker
- Would you pay Microsoft for extended Windows 7 support?

- Firefox 66 has PowerPoint and Word bugs (Fix available)
- AdGuard 3.0 for Android: Redesign, Stealth Mode, Custom Filter Lists
- If you don't want end of support notifications on Windows 7, block KB4493132
- Windows 10 1809: full rollout begins
- A look at BleachBit 2.2
- FixBee, Disk Cleanup and Optimization Software
- Privacy Agent, Remove History Traces From All Browsers
- Windows 10 updates: KB4489894, KB4489890, KB4489888 and KB4489889
- Opera 51 for Android launches with built-in VPN
- Firefox 66.0 Release Information

Ghacks is a technology news blog that was founded in 2005 by Martin Brinkmann. It has since then become one of the most popular tech news sites on the Internet with five authors and regular contributions from freelance writers.

© 2019 gHacks Technology News. All Rights Reserved.

johnwoosaid on September 21, 2011 at 9:30 am“So the hex number 8FA4 becomes in binary 1000.1111.1011.0100.” … A is 1010.. not 1011.

Defiantsaid on September 21, 2011 at 8:20 pmThis is one of the worst articles I have ever read.

So many inaccuracies, typos, and grammar issues…wow.

1) “It’s gets more complex…”

2) “…split each hex character into it’s binary equivalent”.

“it’s”? Really?

3) “8FA4 is actually 36,788 in decimal”…ehhh…no, it’s 36,772 in decimal.

4) If you have a hexadecimal number that you want to convert to decimal, you don’t have to convert it to binary first.

8FA4 in decimal is 8*16^3 + 15*16^2 + 10*16 + 4 = 36,772.

Even if you chose to convert to binary first, your explanation is severely lacking and unclear.

5) “the third is sixteen’s to the power 3”.

“sixteen”, not “sixteen’s”.

6) “If you work it out, the largest number you can have with six hex digits is 17,895,696”. No… FFFFFF = 16,777,215.

Horrific.

Defiantsaid on September 21, 2011 at 9:44 pm“Nearly eighteen million colors represented by only six characters.” should now be “Nearly seventeen million colors represented by only six characters.”

BlueRajasaid on September 21, 2011 at 11:29 pmSlow news day?

Robsaid on September 23, 2011 at 9:33 amhere is an on-line web app that makes it easy to learn about binary and hexadecimal numbers.

http://justwebware.com/bitwise/bitwise.html

Martin Brinkmannsaid on September 23, 2011 at 9:48 amThanks for posting Rob, great find.

Anonymoussaid on October 23, 2012 at 11:41 amThank You for your tutorial Melanie it was very helpful, also; Thank you Defiant for helping with some unclear examples and showing how to convert hexadecimal to decimal without taking it back to binary code.