# Why Is There a Difference When Converting Hexadecimal to Decimal?

• znaya
In summary, the conversation discusses converting 0xC4630000 to decimal and the attempts made to do so. The first attempt uses a calculator and the second attempt manually converts to binary and back to decimal. The discrepancy in the results is found to be due to a miscalculation by the calculator in the second attempt.
znaya

## Homework Statement

Convert 0xC4630000 to decimal.

## 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.

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

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"!

## What is hexadecimal and decimal?

Hexadecimal is a base-16 number system that uses 16 symbols to represent numbers, while decimal is a base-10 number system that uses 10 symbols to represent numbers.

## Why do we need to convert hexadecimal to decimal?

Hexadecimal is often used in computer programming and digital systems, while decimal is used more commonly in everyday life. Converting between the two allows for easier communication and understanding between these systems.

## What is the process of converting hexadecimal to decimal?

To convert hexadecimal to decimal, each digit in the hexadecimal number is multiplied by its corresponding power of 16, starting from the rightmost digit. The results are then added together to get the decimal equivalent.

## Can you provide an example of converting hexadecimal to decimal?

For example, to convert the hexadecimal number 3F to decimal, we multiply the first digit, 3, by 16^1 and the second digit, F, by 16^0. This gives us (3*16^1) + (15*16^0) = 48 + 15 = 63 in decimal.

## What are some common mistakes when converting hexadecimal to decimal?

Some common mistakes include forgetting to multiply the digits by their corresponding powers of 16, not accounting for the letters A-F in the hexadecimal system, and not properly adding the results together.

Replies
2
Views
10K
Replies
1
Views
1K
Replies
5
Views
2K
Replies
2
Views
2K
Replies
2
Views
4K
Replies
2
Views
13K
Replies
7
Views
2K
Replies
1
Views
6K
Replies
1
Views
2K
Replies
2
Views
2K