My Math Forum Hex to decimal conversion

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 September 18th, 2017, 11:14 AM #1 Member   Joined: Aug 2017 From: India Posts: 54 Thanks: 2 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 06:52 AM.
 September 18th, 2017, 11:32 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 I fear that there is no shortcut to doing it manually.
September 18th, 2017, 04:03 PM   #3
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 Originally Posted by MathsLearner123 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.
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 06:53 AM.

 September 18th, 2017, 11:15 PM #4 Senior Member   Joined: Apr 2014 From: UK Posts: 954 Thanks: 341 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 18th, 2017, 11:48 PM   #5
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 Originally Posted by weirddave 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)
I only noticed the additions to the built in calc the other week. It's quite nice!

 September 19th, 2017, 03:58 AM #6 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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 08:42 AM.
 September 19th, 2017, 11:45 PM #7 Senior Member   Joined: Apr 2014 From: UK Posts: 954 Thanks: 341 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 Thanks from Country Boy
 September 20th, 2017, 04:48 AM #8 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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, 02:17 AM #9 Senior Member   Joined: Apr 2014 From: UK Posts: 954 Thanks: 341 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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