Why Is There a Difference When Converting Hexadecimal to Decimal?

[znaya]

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.

 

[cpscdave]

231 + 230 + 226 + 222 + 221 + 217 + 216 =
= 2147483647 + 1073741824 + 67108864 + 4194304 + 2097152 + 131072 + 65536

You sure about all these??

 

[znaya]

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.

 

[cpscdave]

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!

 

[znaya]

:-) I can't believe the time I wasted on this... I was going crazy, already doubting of my skills...
Thanks again.

 

[HallsofIvy]

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