Why Is There a Difference When Converting Hexadecimal to Decimal?

AI Thread Summary
The discussion revolves around the conversion of the hexadecimal number 0xC4630000 to decimal, highlighting a discrepancy in results between two methods. The first attempt yielded a decimal value of 3,294,822,400, while the second method, converting to binary and back to decimal, resulted in 3,294,822,399. The error was traced back to a miscalculation of 2^31, where a calculator incorrectly returned 2^31 as 2,147,483,647 instead of the correct value of 2,147,483,648. This discrepancy led to confusion, emphasizing the importance of verifying calculator outputs. Ultimately, the discussion underscores the need for careful checking in mathematical conversions to avoid errors.
znaya
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Homework Statement


Convert 0xC4630000 to decimal.

Homework Equations



The Attempt at a Solution



First attempt:
0xC4630000

12(167) = 12(268435456) = 3221225472
4(166) = 4(16777216) = 67108864
6(165) = 6(1048576) = 6291456
3(164) = 3(65536) = 196608
0(163) = 0(4096) = 0
0(162) = 0(256) = 0
0(161) = 0(16) = 0
0(160) = 0(1) = 0

3221225472 + 67108864 + 6291456 + 196608 = 3294822400
Ok, google tells me this result is right. But then I tried to convert to binary and from binary to decimal.

Second attempt:

C = 1100
4 = 0100
6 = 0110
3 = 0011
0 = 0000
0 = 0000
0 = 0000
0 = 0000

So, 0xC4630000 = 1100 0100 0110 0011 0000 0000 0000 0000
231 + 230 + 226 + 222 + 221 + 217 + 216 =
= 2147483647 + 1073741824 + 67108864 + 4194304 + 2097152 + 131072 + 65536 = 3294822399

I can't understand why this is failing... Shouldn't the result be the same? Why is there a difference of 1?
Thanks in advance for any help.
 
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znaya said:
231 + 230 + 226 + 222 + 221 + 217 + 216 =
= 2147483647 + 1073741824 + 67108864 + 4194304 + 2097152 + 131072 + 65536

You sure about all these??
 
google says it's wrong!
OMG, just found the error! My calculator returns 231 = 2147483647
But google returns 231 = 2147483648.
The error is exactly there. The calculator miscalculates 231!
I repeated the sum hundreds of times but always using the same calculator...

Thanks.
 
znaya said:
The error is exactly there. The calculator miscalculates 231!

Its a mistake I made all the time, you can't just blindly accept what the calculator tells you. The clue in was you had an even binary number (LSB is 0) and you were getting an odd number. Then you see that one of your other powers is odd.
But hey at least you found out now. I found out one of my calculators had died and was giving wrong answers after my last exam one semester. I spoke to the prof later, cause he couldn't understand how I did all the steps right but kept getting wrong answers :) Luckily the partial points were enough to pass the test, and passing was all I needed for a decent mark!
 
:-) I can't believe the time I wasted on this... I was going crazy, already doubting of my skills...
Thanks again.
 
You should have noticed immediately that 2 to any power cannot end in "7"!
 
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