Two's Complement of fractional numbers

Question

I've been searching around the web for a solution for this question for several weeks but without any success.

My University professor told me that to convert a binary number with a fractional part to a negative number in Two's complement we must do this:

1)Convert the number from base 10 to base 2 (+4.25) = (0100.0100)

2)The only part we need to convert in two's complement right now is the part before the point.

0100 -> 1011 -> 1011 + 1 -> 1100

So for him, -4.25 in two's complement is (1100.0100) without any conversion for the fractional part.

For me, this solution is wrong because if we try to add up these two numbers we get

0100.0100 + 1100.0100 = 0000.1000

that's 0.5 not 0

Answer 1

Your professor is simply wrong.

This statement refers to a negative value with a fractional part: "The two’s complement representation is formed by inverting the bits of the absolute value and adding a 1 to the least significant (rightmost) bit."

• Sarah L. Harris, David Harris, in Digital Design and Computer Architecture, 2022 Chapter 5.3.1 Fixed-Point Number Systems The LSB is located on the fractional part. So even the fractional part changes, unless it just a sequence of 0s.

Moreover, Fixed-Point is usually stored in microprocessors as integers, where you as a programmer must know where the point is and where it moves (e.g. in multiplications). The CPU does not know it is a fixed point value and treats it as an integer.

Answer 2

For a fraction you do exactly the same as a normal integer, meaning invert all the bits and +1 to the Least significant bit for your representation:
4.25 = 0100.0100
-4.25 = 1011.1100
Also can't come up with anything your professor could have meant.