Re: Arithmetics with carry

If I remember right, this is a counter application.
Forget the 16-bit ALU and use a 32-bit counter instead, and avoid all
this headache. KISS.
Peter Alfke
==========================
Glen Herrmannsfeldt wrote:
> 
> "Kevin Becker" <[EMAIL PROTECTED]> wrote in message
> news:[EMAIL PROTECTED]
> > Francisco Rodriguez wrote:
> > > As your numbers are 32-bit wide, and overflow condition is a flag
> > > about the result of the _whole_ v := v + i operation, it can be
> determined
> > > by the MSB bits only (that is, from columns 31 and 30 of the addition).
> >
> > Thank you! I think I used the wrong word "underflow". What I mean is:
> > if "i" is negative, it might be that abs(lo(i)) is greater than lo(v).
> 
> Yes, underflow is the right word.  It isn't used very often, though.
> 
> > What happens then? An example:
> >
> > v = 1234 0100 hex
> > i = 0000 0101 hex
> >
> > The operation for the lo bits will result in FFFF and the carry will
> > be set. Then when I add the high bits, it will be 1235 when it should
> > actually be 1233. How do I save that the first operation was not an
> > overflow but a borrow? (I don't know how to call this. That's what I
> > mistakenly called underflow).
> 
> Hmm.  X'0100' + X'0101' is X'0201' with no overflow.  If you want to add a
> small twos complement negative number, then that number will have F's in the
> high bits which will take care of the 1233 part.   In that case, borrow
> means that there is no carry, otherwise there is a carry.  Say v=X'12340100'
> and i is negative 257.  Negative 257 is X'FFFFFEFF'
> 
> X'0100' + X'FEFF' is X'FFFF' with no carry.   X'1234'+X'FFFF' is X'1233'
> with carry.   The carry into the high bit is also 1, so that there is no
> overflow or underflow.
> 
> > Glen Herrmannsfeld wrote:
> > > After the high halfword add, you compare the carry out to the carry out
> of
> > > the sign bit to the carry in of the sign bit.  If they are different
> then it
> > > is overflow or underflow.  The value of such bit tells you which one.
> >
> > So does that mean I have to modify my architecture and set TWO flags?
> > A carry flag and a negative flag (if sign of last operation was
> > negative), and then the Add-With-Carry instruction would look at both?
> 
> No, add with carry doesn't need to know.   You only need the two flags at
> the end if you want to detect overflow and underflow.
> 
> -- glen