how to convert negative hexadecimal to decimal

Question

hi I want to know how it is possible to convert a hexadecimal negative value (to complement encoding) to decimal, easily without converting hexadecimal to binary and then multiplying each bit in by a power of 2 and sums all the value to get the result, it takes too much time : example of number (32 bits) : 0xFFFFFE58

so how can I do it?

Solution

without using a computer you can calculate it like this:

0xFFFF FE58 = - 0x1A8 = -(1 * 16² + 10 * 16 + 8) = -(256 + 160 + 8) = -424

0xFFFF FE58 is a negative number in 2's complement. To get the absolute value you have to invert all bits and add 1 in binary. You also can subtract this number from the first number out of range (0x1 0000 0000)

 0x100000000
-0x0FFFFFE58
      =
 0x0000001A8

now we know that your number is -0x1A8. now you have to add up the digits multiplied with their place value. 8 * 16^0 + A (which is 10) * 16^1 + 1 * 16^2 = 424. So the decimal value of your number is -424.

Comments

[mch]

I added a little bit. I hope this makes it clearer. Please ask what´s unclear.