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Convert hexadecimal to decimal

  1. Jun 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Convert 0xC4630000 to decimal.

    2. Relevant equations

    3. 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.
     
  2. jcsd
  3. Jun 17, 2015 #2
    You sure about all these??
     
  4. Jun 17, 2015 #3
    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.
     
  5. Jun 17, 2015 #4
    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!
     
  6. Jun 17, 2015 #5
    :-) I can't believe the time I wasted on this... I was going crazy, already doubting of my skills...
    Thanks again.
     
  7. Jun 17, 2015 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You should have noticed immediately that 2 to any power cannot end in "7"!
     
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