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September 18th, 2017, 12:14 PM  #1 
Newbie Joined: Aug 2017 From: India Posts: 6 Thanks: 0  Hex to decimal conversion
I know how to convert hex to decimal and vice versa. So many times in my work I have to convert from hex to decimal, and I always use a calculator. Are there any simple methods to do it without a calculator? Sorry if the question is not related to here.
Last edited by skipjack; September 21st, 2017 at 07:52 AM. 
September 18th, 2017, 12:32 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 857 Thanks: 348 
I fear that there is no shortcut to doing it manually.

September 18th, 2017, 05:03 PM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,454 Thanks: 489 Math Focus: Yet to find out.  If you're doing it that regularly, maybe get an app on your phone instead of using a calculator.
Last edited by skipjack; September 21st, 2017 at 07:53 AM. 
September 19th, 2017, 12:15 AM  #4 
Senior Member Joined: Apr 2014 From: UK Posts: 786 Thanks: 294 
I use the windows calculator, it has a programming mode where you can swap between hex and decimal numbers on the fly. I use it often and just leave it open (I usually have 2 or 3 open if I'm honest, lol)

September 19th, 2017, 12:48 AM  #5 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,454 Thanks: 489 Math Focus: Yet to find out.  I only noticed the additions to the built in calc the other week. It's quite nice!

September 19th, 2017, 04:58 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,875 Thanks: 766 
To convert from decimal to hex, divide by 16. For example, 3244, divided by 16, is 202.75  that is, quotient 202 with remainder 12. 3244 = (202)(16) + 12. 202, divided by 16, is 12.625  that is, quotient 12 with remainder 10. 202 = 12(16) + 10, so 3244 = (12(16) + 10)(16) + 12 = 12(16^2) + 10(16) + 12. Writing 10 = A and 12 = C, that is CAC in hexadecimal. Going from hexadecimal to decimal would be the same thing if we could easily divide in hexadecimal. If not, use the definition of hexadecimal: 3A2F in hexadecimal is $\displaystyle 3(16^3)+ 10(16^2)+ 2(16)+ 15= 3(4096)+ 10(256)+ 32+ 15= 12288+ 2560+ 32+ 15= 14895$ in decimal. Last edited by skipjack; September 19th, 2017 at 09:42 AM. 
September 20th, 2017, 12:45 AM  #7 
Senior Member Joined: Apr 2014 From: UK Posts: 786 Thanks: 294 
That example is exactly why I use the windows calculator, I only have to input one set of digits one time, which is the only time I can introduce an error. (I could of course input a hex number such as 1234 while in decimal mode and accidentally convert that to hex, instead of the other way round). When I have had to do it manually, I start from the left (using 3A2F as the example): 3 There's a digit to its right, so multiply by 16 then add the next digit (3*16) + A = 58 There's a digit to its right, so multiply by 16 then add the next digit (58*16) + 2 = 930 There's a digit to its right, so multiply by 16 then add the next digit (930*16) + F = 14895 No more digits so we have the answer 
September 20th, 2017, 05:48 AM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,875 Thanks: 766 
weirddave's weird method works because 3(16^3)+ 10(16^2)+ 2(16)+ 15= (3(16)+ 10)(16^2)+ 2(16)+ 15= (3(16)+ 10(16)+ 2)(16)+ 15.

September 21st, 2017, 03:17 AM  #9 
Senior Member Joined: Apr 2014 From: UK Posts: 786 Thanks: 294 
It's also easier to do with a calculator, because you are always working with the last result rather than calculating each part separately then adding them, really long strings of Hex are easy, if you use the 16^n method there are a lot of numbers to add up at the end. The last part in CBs post above should be (((3(16)+10)(16)+2)(16)+15 Another way to explain how it works is that the 3 is multiplied by 16 3 times during the calculation process, which is the same as 16^3, the 10 is multiplied 2 times during the process (16^2) and the 2 by 16 once. 

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conversion, decimal, hex 
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