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Converting from hexadecimal using two's compliment

Posted on 2014-04-19
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What are the steps you would take to convert a hexadecimal number such as 0x0AB00000 to a decimal number, knowing that it is an unsigned integer. Are there different steps to convert this number if you knew that it was two's compliment instead of an unsigned integer?
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Question by:pcomb
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ChloesDad earned 2000 total points
ID: 40010525
Yes,

The first step is the same either way as you need to convert the hex number to binary

In your example it is

00001010 10110000 00000000 00000000

This converts to a positive decimal value of 179306496

For a two's compliment, the most significant bit defines the sign, in this case, its 0 so its a positive number.

If we ignored your leading 0 in the hex string, and it was AB00000 then the first 4 0's are now not present and the most significant bit is now a 1 indicating a negative number.

The decimal value of the remaining bits is 45088768, and to get the negative value we subtract this value from 2^N where N is the number of bits in the original number (28)

2^28 = 268435456

so number = 268435456 - 45088768 = -223346688

Using a simpler example

10000000 = 2^8 - 0 = -128
11111111 = 2^8 - 127 = -1
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by:skullnobrains
ID: 40011081
$ echo 'ibase=16 ; ob=10 ; 0AB00000' | bc
179306496
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