# Hexadecimal to Decimal and Binary **URL:** \ **Category:** Lessons Discussion\ **Created:** [December 29, 2016, 5:13pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221 "2016-12-29T17:13:21Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![ReneMolenaar](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/renemolenaar/32/488_2.png) [@ReneMolenaar](https://forum.networklessons.com/u/ReneMolenaar)\ **Post date:** [December 29, 2016, 5:13pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/1 "2016-12-29T17:13:21Z")
This topic is to discuss the following lesson: > **[Hexadecimal to Decimal and Binary](https://networklessons.com/subnetting/hexadecimal-decimal-binary)** > > This lesson explains how to calculate from decimal to binary and hexadecimal. ---
**Author:** ![ranjithasivakami](https://cdn-forum.networklessons.com/letter_avatar_proxy/v4/letter/r/ba9def/32.png) [@ranjithasivakami](https://forum.networklessons.com/u/ranjithasivakami)\ **Post date:** [October 21, 2015, 6:25pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/2 "2015-10-21T18:25:03Z")
How to convert IPV6 to IPV4 address? ---
**Author:** ![ReneMolenaar](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/renemolenaar/32/488_2.png) [@ReneMolenaar](https://forum.networklessons.com/u/ReneMolenaar)\ **Post date:** [October 21, 2015, 7:09pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/3 "2015-10-21T19:09:55Z")
We can’t, there is no such thing 🙂 IPv6 addresses are 128 bit and hexadecimal, IPv4 has 32 bit decimal addresses. ---
**Author:** ![deruitermathijs](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/deruitermathijs/32/221_2.png) [@deruitermathijs](https://forum.networklessons.com/u/deruitermathijs)\ **Post date:** [January 13, 2016, 4:26pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/4 "2016-01-13T16:26:52Z")
Typo: “The first nibble will be 8 + 4 = 12. The decimal value 7 is C in hexadecimal.” ---
**Author:** ![ReneMolenaar](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/renemolenaar/32/488_2.png) [@ReneMolenaar](https://forum.networklessons.com/u/ReneMolenaar)\ **Post date:** [January 13, 2016, 4:29pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/5 "2016-01-13T16:29:04Z")
Thanks Mathijs, it has been fixed. ---
**Author:** ![jorotz](https://cdn-forum.networklessons.com/letter_avatar_proxy/v4/letter/j/3ec8ea/32.png) [@jorotz](https://forum.networklessons.com/u/jorotz)\ **Post date:** [March 12, 2016, 6:05am UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/6 "2016-03-12T06:05:18Z")
Hi Rene, “In the decimal system we count from 1-10, in the hexadecimal system we count from 1 – F” should be “decimal 0-9, hexadecimal 0-F” 🙂 ---
**Author:** ![ReneMolenaar](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/renemolenaar/32/488_2.png) [@ReneMolenaar](https://forum.networklessons.com/u/ReneMolenaar)\ **Post date:** [March 12, 2016, 3:21pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/7 "2016-03-12T15:21:05Z")
Hi Georgi, That is so true, especially for computers 😉 Just edited the post…thanks! Rene ---
**Author:** ![emil.qasimov](https://cdn-forum.networklessons.com/letter_avatar_proxy/v4/letter/e/ecb155/32.png) [@emil.qasimov](https://forum.networklessons.com/u/emil.qasimov)\ **Post date:** [June 25, 2019, 6:20pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/8 "2019-06-25T18:20:29Z")
Hi Rene , I don’t understand how you convert nibbles binary to decimal, ---
**Author:** ![lagapidis](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/lagapidis/32/4949_2.png) [@lagapidis](https://forum.networklessons.com/u/lagapidis)\ **Post date:** [June 26, 2019, 2:35pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/9 "2019-06-26T14:35:52Z")
Hello Emil First of all let’s see the relationships between hex, and a nibble in binary. Each single hex digit corresponds to four bits in binary. But four bits in binary is considered a nibble. So a single hex digit corresponds to a nibble in binary. So when you are dealing with nibbles, it’s good to remember that you are dealing with four digits in binary, or one digit in hex. If you know that, then it’s easy to convert from hex to decimal and decimal to hex. But when you convert from hex to binary, it’s usually easier to go from hex to decimal (which is trivial) to binary. The same when you go in the other direction, that is binary, to decimal to hex. So let’s say you have the hex digit **B**. This corresponds to **11** in decimal. Which corresponds to **1011** (8+0+2+1=11) in binary, which is a nibble. An example in the other direction could be **1110**. This is 8+4+2= **14** in decimal, which corresponds to **E**. I hope this has been helpful! Laz ---
**Author:** ![gazwoz](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/gazwoz/32/596_2.png) [@gazwoz](https://forum.networklessons.com/u/gazwoz)\ **Post date:** [November 12, 2019, 4:00pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/10 "2019-11-12T16:00:24Z")
Chaps, I’ve been writing out the place value systems for binary, decimal and hexadecimal and have spotted a pattern that I can’t explain. For instance.. In Binary - 2 ^ 3 = 1000 In Decimal - 10 ^ 3 = 1,000 In Hexadecimal - 16 ^ 3 = 1000 All results are 1000 even though this is expressed in the three different number systems so are different values. The pattern repeats no matter what the next power of is: In Binary - 2 ^ 7 = 10000000 In Decimal - 10 ^ 7 = 10,000,000 In Hexadecimal - 16 ^ 7 = 10000000 This is more of an observation that a question I suppose but if anyone can offer an explanation as to why this occurs then I’d appreciate it! Cheers, Gareth. ---
**Author:** ![lagapidis](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/lagapidis/32/4949_2.png) [@lagapidis](https://forum.networklessons.com/u/lagapidis)\ **Post date:** [November 13, 2019, 6:37am UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/11 "2019-11-13T06:37:19Z")
Hello Gareth Just to clarify, I assume you mean the following: - In binary: 2^3 means 10 X 10 X 10 = 1000 - In decimal: 10^3 means 10 X 10 X 10 = 1000 - in Hex: 16^3 means 10 X 10 X 10 = 1000 You’ll notice that the number 2 expressed in binary is 10, the number 10 in decimal is 10, and the number 16 expressed in hex is also 10. When you apply multiplication to the number 10 in any base system (binary, trinary, decimal, hex, or literally any base), you will always use the same methodology to multiply. Specifically, you will simply append zeros at the end. This is a pattern that appears because of the fact that you are using the base value of each system (2 for binary, 10 for decimal, 16 for hex) in your calculation. This results in using the same symbols for all three numbers, which when multiplied results in the same symbols once again since the same process (multiplication) is applied in each case. I hope this has been helpful! Laz ---
**Author:** ![gazwoz](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/gazwoz/32/596_2.png) [@gazwoz](https://forum.networklessons.com/u/gazwoz)\ **Post date:** [November 13, 2019, 2:03pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/12 "2019-11-13T14:03:25Z")
Wow! And the number 1 in binary, decimal and hexadecimal is always 1 too… hmmmmm Sounds so obvious when you type it out (but it definitely still blows my mind somewhat). I’m also trying to bend my mind around the fact that any number ^1 is always 1… Thanks Laz - this is a great help. ---
**Author:** ![lagapidis](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/lagapidis/32/4949_2.png) [@lagapidis](https://forum.networklessons.com/u/lagapidis)\ **Post date:** [November 13, 2019, 3:35pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/13 "2019-11-13T15:35:56Z")
Hi Gareth I think you meant any number ^0 is always 1, right? Any number ^1 is simply itself. But it is quite interesting, this world of mathematics isn’t it!?!?! Laz ---
**Author:** ![gazwoz](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/gazwoz/32/596_2.png) [@gazwoz](https://forum.networklessons.com/u/gazwoz)\ **Post date:** [November 13, 2019, 3:40pm UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/14 "2019-11-13T15:40:16Z")
🙂 Yep - any number to the ^0 is 1 - my bad!!! ---
**Author:** ![awais3859](https://cdn-forum.networklessons.com/letter_avatar_proxy/v4/letter/a/0ea827/32.png) [@awais3859](https://forum.networklessons.com/u/awais3859)\ **Post date:** [August 23, 2026, 11:16am UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/15 "2026-08-23T11:16:30Z")
Even though the conversion from decimal to hexadecimal is correct. The image of the last nibble shows a decimal value of 6 not 14. Can this be looked into? ![Screenshot From 2026-08-23 12-12-24](https://cdn-forum.networklessons.com/uploads/default/original/2X/9/9779ec8ea228c9aa896a7fd70b3ecf5a0d8a17cc.png) ---
**Author:** ![lagapidis](https://cdn-forum.networklessons.com/user_avatar/forum.networklessons.com/lagapidis/32/4949_2.png) [@lagapidis](https://forum.networklessons.com/u/lagapidis)\ **Post date:** [August 27, 2026, 7:16am UTC](https://forum.networklessons.com/t/hexadecimal-to-decimal-and-binary/1221/16 "2026-08-27T07:16:02Z")
Hello Awais! Indeed, the last line should read: > The second nibble will be 4 + 2 = 6. The decimal value 6 is 6 in hexadecimal. Thanks for pointing that out. I will let @ReneMolenaar know to take a look and make the corrections. Laz