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September 18th, 2017, 11:14 AM   #1
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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.
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September 18th, 2017, 11:32 AM   #2
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I fear that there is no shortcut to doing it manually.
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September 18th, 2017, 04:03 PM   #3
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Originally Posted by MathsLearner123 View Post
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.
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September 18th, 2017, 11:15 PM   #4
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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)
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September 18th, 2017, 11:48 PM   #5
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Originally Posted by weirddave View Post
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!
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September 19th, 2017, 03:58 AM   #6
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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.
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September 19th, 2017, 11:45 PM   #7
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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
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September 20th, 2017, 04:48 AM   #8
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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.
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September 21st, 2017, 02:17 AM   #9
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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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