Unsigned to signed vector.

u(7)

unsigned =3D> signed

What I want to do is :

unsigned min: 0000000000 => signed min: 1 000001 => integer min :

-127 unsigned max: 1111111111 => signed max: 0 1111111 => integer max : 127

You didn't tell us that :-)

Do you also want linear scaling between these two endpoints? I guess so. Let's start again.

You have unsigned input U in the range [0,1023].

You have signed output S in the range [-127, +127]. I don't know why you choose to exclude -128, but hey, that's OK.

So what do you want to do?

S = U/4 - 127

is pretty close, I think, if U/4 is taken to mean the whole-number part of the result (throw away the fraction). But unfortunately, 1020/4 = 255 and 255-127 = 128, so you'll get +128 rather than +127 as the upper limit. If you can accept -128 as the lower limit (this is the true minimum value of a signed 8-bit) then you can do

S = U/4 - 128

and all is well. Now, U/4 is simply the eight most significant bits of U; and -128 is easily done by just flipping the MSB; so

so, I return to my first message, that is correct :

if ( unsigned_data =3D "00000000" ) then signed_data

No, it's not; you're being unacceptably careless.

This test will never be true, because unsigned_data is

And now you're trying to copy a 10-bit expression into an 8-bit result.

But yes, you're on the right track.

Always true, usually ignored!