# sign magnitude, ones complement, two's complement

Discussion in 'C Programming' started by Mantorok Redgormor, Oct 5, 2003.

1. ### Mantorok RedgormorGuest

From least to greatest is it

sign magnitude
ones complement
two's complement

Where sign magnitude is the least way to represent integers
and two's complement is the best way to represent integers?

What are the pitfalls of them?

Mantorok Redgormor, Oct 5, 2003

2. ### Glen HerrmannsfeldtGuest

"osmium" <> wrote in message
news:blq4r0\$f15nv\$-berlin.de...
> Mantorok Redgormor writes:
>
> > sign magnitude
> > ones complement
> > two's complement

>
> > What are the pitfalls of them?

>
> I doubt if sign magnitude has ever been used in a popular US computer.

The
> disadvantage of ones complement is that there are two representations for

0,
> "positive" zero and negative zero. OTOH subtraction is less onerous with

a
> ones complement hardware design.

I believe the IBM 7090. But then they internally convert to ones complement

Multiply and divide are easier in sign magnitude, and I believe divide is
done that way on most computers now.

> Two's complement is certainly the dominant form in current computers.

Except for those made by Univac.

-- glen

Glen Herrmannsfeldt, Oct 6, 2003

3. ### osmiumGuest

Mantorok Redgormor writes:

> sign magnitude
> ones complement
> two's complement

> What are the pitfalls of them?

I doubt if sign magnitude has ever been used in a popular US computer. The
disadvantage of ones complement is that there are two representations for 0,
"positive" zero and negative zero. OTOH subtraction is less onerous with a
ones complement hardware design.

Two's complement is certainly the dominant form in current computers.

osmium, Oct 6, 2003
4. ### Gordon BurdittGuest

>From least to greatest is it

Least to greatest *WHAT*? Number of transistors in the CPU
to implement it? Tax rate? Weight of the documentation?

>sign magnitude
>ones complement
>two's complement
>
>Where sign magnitude is the least way to represent integers
>and two's complement is the best way to represent integers?

Which is better, rat poison, a condom, or a Pepsi? It does rather
depend on what you want it for.

>What are the pitfalls of them?

Unless you are designing a CPU or selecting one to buy, you don't
get to choose, and there are many MANY factors much more important
than this (like availability of a good compiler for it).

Gordon L. Burditt

Gordon Burditt, Oct 6, 2003
5. ### osmiumGuest

Glen Herrmannsfeldt writes:

> > I doubt if sign magnitude has ever been used in a popular US computer.

> I believe the IBM 7090. But then they internally convert to ones

complement
> to do addition and subtraction.

I'll be damned! And also the 7094 according to this link. Just to cloud
the issue they use twos complement for some index fiddling if you look at
the instruction repertoire; which is also on this site.

http://www.frobenius.com/binary.htm

osmium, Oct 6, 2003
6. ### CBFalconerGuest

osmium wrote:
> Mantorok Redgormor writes:
>
> > sign magnitude
> > ones complement
> > two's complement

>
> > What are the pitfalls of them?

>
> I doubt if sign magnitude has ever been used in a popular US
> computer. The disadvantage of ones complement is that there are
> two representations for 0, "positive" zero and negative zero.
> OTOH subtraction is less onerous with a ones complement hardware
> design.
>
> Two's complement is certainly the dominant form in current
> computers.

Actually arithmetic is more convenient in 2's complement, because
there is no need for end-around-carries.

However negation of a value is simpler in 1's complement. By
making the basic arithmetic operation a subtractor (rather than an
adder) you can avoid negative zero ever appearing, thus allowing
use of that value as a trap (e.g. uninitialized).

--
Chuck F () ()
Available for consulting/temporary embedded and systems.

CBFalconer, Oct 6, 2003
7. ### Eric SosmanGuest

osmium wrote:
>
> Mantorok Redgormor writes:
>
> > sign magnitude
> > ones complement
> > two's complement

>
> > What are the pitfalls of them?

>
> I doubt if sign magnitude has ever been used in a popular US computer.

The first computer I ever programmed used signed magnitude.
Was it "popular?" Hard to tell, but IBM thought enough of the
design to build the machines and offer them in a range of sizes
(twenty, forty, or sixty thousand decimal digits of memory).

--

Eric Sosman, Oct 6, 2003
8. ### Joe WrightGuest

Eric Sosman wrote:
>
> osmium wrote:
> >
> > Mantorok Redgormor writes:
> >
> > > sign magnitude
> > > ones complement
> > > two's complement

> >
> > > What are the pitfalls of them?

> >
> > I doubt if sign magnitude has ever been used in a popular US computer.

>
> The first computer I ever programmed used signed magnitude.
> Was it "popular?" Hard to tell, but IBM thought enough of the
> design to build the machines and offer them in a range of sizes
> (twenty, forty, or sixty thousand decimal digits of memory).
>

Upthread, someone mentioned the last might have been the IBM 7094 which
came out in Jan 1963 and was the last of the 'Old Iron' before the
'Modern' IBM 360 and later. How 'popular' could the 7094 have been? How
many of them were built? I don't know the number. 100? More?

My first computer was the Philco 2000/212 which came out the same month
as the 7094. In long suit we had 32K of 48-bit (8-character) words of
RAM in four 8K banks. Each bank had a cycle time of 1.1 microseconds.
Bank selection was done in the low order two bits of address so that we
could get four 48-bit words every 1.1 usecs. This was 'core' memory with
real magnetic cores.

We left the 7094 for dead.

Philco Computers, Willow Grove, PA, R.I.P.
--
Joe Wright http://www.jw-wright.com
"Everything should be made as simple as possible, but not simpler."
--- Albert Einstein ---

Joe Wright, Oct 7, 2003
9. ### Glen HerrmannsfeldtGuest

"CBFalconer" <> wrote in message
news:...
> osmium wrote:
> > Mantorok Redgormor writes:
> >
> > > sign magnitude
> > > ones complement
> > > two's complement

> >
> > > What are the pitfalls of them?

(snip)

> > Two's complement is certainly the dominant form in current
> > computers.

>
> Actually arithmetic is more convenient in 2's complement, because
> there is no need for end-around-carries.

With popular adder designs end-around carry isn't hard to do, and shouldn't
be slower. It complicates serial adders, but since the PDP-8S I don't know
that there have been any machines with serial binary adders.

> However negation of a value is simpler in 1's complement. By
> making the basic arithmetic operation a subtractor (rather than an
> adder) you can avoid negative zero ever appearing, thus allowing
> use of that value as a trap (e.g. uninitialized).

Yes, negation can be complicated with two's complement, as it can overflow.
On some machines this means processing a trap or exception for that case.

-- glen

Glen Herrmannsfeldt, Oct 8, 2003