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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?
867
The hexadecimal value of a negative decimal number can be obtained starting from the binary value of that decimal number positive value. The binary value needs to be negated and then, to add 1. The result (converted to hex) represents the hex value of the respective negative decimal number.
Given hexadecimal number is 7CF. To convert this into a decimal number system, multiply each digit with the powers of 16 starting from units place of the number. From this, the rule can be defined for the conversion from hex numbers to decimal numbers.
My book says the hexadecimal notation FFFF equals 65535 in decimal value.
The simplest is to simply use the leftmost digit of the number as a special value to represent the sign of the number: 0 = positive, 1 = negative. For example, a value of positive 12 (decimal) would be written as 01100 in binary, but negative 12 (decimal) would be written as 11100.
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.
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