How can I convert signed binary fraction to signed decimal?

Isn't 1.11010 negative? For example when we have 10010 signed, then it is equal to -14 not 16 (which is the sign and magnitude).

You mean you're interpreting the first bit as the sign bit ? Why is that ? Why not simply write the sign out, like :

        - 0.11010

?

Or are you somehow trying to look at how a computer stores such values ?

In the end it doesn't really matter whether you use a minus sign, or interpret the first bit as a sign bit. The result is exactly the same. It's just a lot clearer to use the minus sign for theoretical exercises. Hence my confusion ;)

It's not simply the fisrt bit is sign bit.

1.11010 is NOT equal to -0.11010

it IS equal to -0.00110 (which is the inverse of 1.11010 that is found by applying 1's complement and then adding 1.)

So, -0.00110b(s&m)=-0.1875d=1.11010(signed)

but what you say, -0.11010=-0.8125

>> It's not simply the fisrt bit is sign bit.

On the site you posted, it's indeed not :)

I still think it's artificial though ;) But that doesn't matter, as you found what you needed to know :)

yeah, it's special to computers and indeed artificial.

What I meant by artificial is that it doesn't serve any immediate practical purpose. It serves as a theoretical exercise and as a step-up point to the way floating point values are stored.

Not really, we can use them in many operations in the area of computer organization. For example Serial Communication Interface (UART), an RS232 transmission, can use signed bits to transfer negative numbers in practice. (We convert the hexadecimal values to binary values while the transfer is in process, this is where we need them).

Moreover any number we use and store in RAM is also stored with their signed conversion, the cost of adding "-" is very much and requires more place than the single sign bit. Thus, we can use them anywhere where we want to save space from memory and make the process faster.

Of course the use of a sign bit is very common. But I was referring to the signed binary fractions representation detailed on the page you linked to. It is not practical, to use that for representing a fraction in a computer. Floating point representation is usually used instead. The range it can represent is more useful, and it has a separate sign bit.

Note that I'm only discussing this because you might find it useful. If that's not the case, then please tell me ;)

I'm also enjoying  the discussion. Yes, you're right, floating points are usually used for fractional numbers since they are more effective than usual binary coded fractions. Implementations may vary according to the need of the system that we are going to build. Floating point notation is preferred because it permits longer numbers to be stored in the memory, since the mantissa of the number is encoded by using the offset values.

Precisely :) I agree that in some cases, and on some platforms, signed binary fractions might be useful.