# 1's complement and 2's complement

Discussion in 'C++' started by sarathy, Aug 1, 2006.

1. ### sarathyGuest

Hi all,
I have a few doubts in the 1's and 2's complement
representation. Generally negative numbers can be represented using
either 1's complement or 2's complement representation.

1's complement ---> reverse all the bits
2's complement ---> reverse all the bits + 1

i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
But when a number and its complement are added the result must be a
zero right ??
But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
Should'nt we be getting a zero as result ???

2's complement of 2 ( 0000 0010 ) is -2 ( 1111 1110 )
Adding we get , 0000 0010 + 1111 1110 = 0000 0000 ==> [ OK]

Does this complement representation have anything to do with the C's ~
[1's complement] operator ?
Is this representation architecture dependent or compiler dependent ?

Regards,
Sarathy

sarathy, Aug 1, 2006

2. ### SM RyanGuest

"sarathy" <> wrote:
# Hi all,
# I have a few doubts in the 1's and 2's complement
# representation. Generally negative numbers can be represented using
# either 1's complement or 2's complement representation.
#
# 1's complement ---> reverse all the bits
# 2's complement ---> reverse all the bits + 1
#
# i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
# But when a number and its complement are added the result must be a
# zero right ??
# But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]

On a ones complement machine, ~0 is 0, called a negative zero.
Some CPUs convert -0 to +0, some don't. -0 = +0, but also
sometimes -0 < +0.

# Does this complement representation have anything to do with the C's ~
# [1's complement] operator ?

On ones complement CPUs, -x = ~x. Whether this was signficant when C
was first created, you would have to ask Ritchie.

--
SM Ryan http://www.rawbw.com/~wyrmwif/
So....that would make Bethany part black?

SM Ryan, Aug 1, 2006

3. ### red floydGuest

sarathy wrote:
> Hi all,
> I have a few doubts in the 1's and 2's complement
> representation. Generally negative numbers can be represented using
> either 1's complement or 2's complement representation.
>
> 1's complement ---> reverse all the bits
> 2's complement ---> reverse all the bits + 1
>
> i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
> But when a number and its complement are added the result must be a
> zero right ??
> But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
> Should'nt we be getting a zero as result ???

In a pure 1's complement notation, you have the concept of "minus zero",
which is the ones complement of 0.

So your result is "minus zero".

red floyd, Aug 1, 2006
4. ### Roy SmithGuest

In article <>,
"sarathy" <> wrote:

> Hi all,
> I have a few doubts in the 1's and 2's complement
> representation. Generally negative numbers can be represented using
> either 1's complement or 2's complement representation.
>
> 1's complement ---> reverse all the bits
> 2's complement ---> reverse all the bits + 1
>
> i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
> But when a number and its complement are added the result must be a
> zero right ??
> But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
> Should'nt we be getting a zero as result ???

You did. In 1's complement, there is no unique representation for zero.
All 0's and all 1's are both equal to zero.

> Does this complement representation have anything to do with the C's ~
> [1's complement] operator ?

Not really

> Is this representation architecture dependent or compiler dependent ?

Whether you are doing 1's complement or 2's complement math depends on the
underlying hardware. That being said, I haven't seen a 1's complement
machine in a couple of eons. It's pretty much an obsolete concept as far
as hardware design goes.

Roy Smith, Aug 1, 2006
5. ### Bill PursellGuest

Roy Smith wrote:
> In article <>,
> "sarathy" <> wrote:

> > 1's complement ---> reverse all the bits
> > 2's complement ---> reverse all the bits + 1
> >
> > i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
> > But when a number and its complement are added the result must be a
> > zero right ??
> > But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
> > Should'nt we be getting a zero as result ???

>
> You did. In 1's complement, there is no unique representation for zero.
> All 0's and all 1's are both equal to zero.

No, in 8-bit ones complement, zero is represented as either
0x00 or 0x80. 0xff is -127.

The problem is that addition with one's complement is
not the same as addition with 2's complement. To
add two numbers, you have to perform different operations
depending on the signedness of the numbers, and that
is why 2's complement is preferred.

Bill Pursell, Aug 1, 2006
6. ### Michael MairGuest

Bill Pursell schrieb:
> Roy Smith wrote:
>>In article <>,
>> "sarathy" <> wrote:

>
>>>1's complement ---> reverse all the bits
>>>2's complement ---> reverse all the bits + 1
>>>
>>>i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
>>>But when a number and its complement are added the result must be a
>>>zero right ??
>>>But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
>>>Should'nt we be getting a zero as result ???

>>
>>You did. In 1's complement, there is no unique representation for zero.
>>All 0's and all 1's are both equal to zero.

>
> No, in 8-bit ones complement, zero is represented as either
> 0x00 or 0x80. 0xff is -127.

8-bit ones complement? You mean sign and magnitude.

There is only one kind of ones complement for C.

C99, 62.6.2#2: "
â€” the corresponding value with sign bit 0 is negated (sign and magnitude);
â€” the sign bit has the value -(2N) (twoâ€™s complement);
â€” the sign bit has the value -(2N - 1) (oneâ€™s complement).
"

> The problem is that addition with one's complement is
> not the same as addition with 2's complement. To
> add two numbers, you have to perform different operations
> depending on the signedness of the numbers, and that
> is why 2's complement is preferred.

And one's complement and sign-magnitude have the advantage
of symmetric value range and others. There have been enough

Cheers
Michael
--
E-Mail: Mine is an /at/ gmx /dot/ de address.

Michael Mair, Aug 1, 2006
7. ### sarathyGuest

Hi,
I guess -0 ==> 1111 1111 is correct in 1's complement notation.
-0 ==> 1000 0000 is in signed magnitude notation.

Please verify and revert back in case.

Rgrds,
Sarathy

Bill Pursell wrote:
> Roy Smith wrote:
> > In article <>,
> > "sarathy" <> wrote:

>
> > > 1's complement ---> reverse all the bits
> > > 2's complement ---> reverse all the bits + 1
> > >
> > > i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
> > > But when a number and its complement are added the result must be a
> > > zero right ??
> > > But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
> > > Should'nt we be getting a zero as result ???

> >
> > You did. In 1's complement, there is no unique representation for zero.
> > All 0's and all 1's are both equal to zero.

>
> No, in 8-bit ones complement, zero is represented as either
> 0x00 or 0x80. 0xff is -127.
>
> The problem is that addition with one's complement is
> not the same as addition with 2's complement. To
> add two numbers, you have to perform different operations
> depending on the signedness of the numbers, and that
> is why 2's complement is preferred.

sarathy, Aug 1, 2006
8. ### Bill PursellGuest

Michael Mair wrote:
> Bill Pursell schrieb:
> > Roy Smith wrote:
> >>In article <>,
> >> "sarathy" <> wrote:

> >
> >>>1's complement ---> reverse all the bits
> >>>2's complement ---> reverse all the bits + 1
> >>>
> >>>i.e 1's complement of 2 ( 0000 0010 ) is -2 ( 1111 1101 )
> >>>But when a number and its complement are added the result must be a
> >>>zero right ??
> >>>But in this case 0000 0010 + 1111 1101 = 1111 1111 ==> [ ?? ]
> >>>Should'nt we be getting a zero as result ???
> >>
> >>You did. In 1's complement, there is no unique representation for zero.
> >>All 0's and all 1's are both equal to zero.

> >
> > No, in 8-bit ones complement, zero is represented as either
> > 0x00 or 0x80. 0xff is -127.

>
> 8-bit ones complement? You mean sign and magnitude.

Oops. Of course.

> of symmetric value range and others. There have been enough

Agreed!!

--
Bill

Bill Pursell, Aug 1, 2006
9. ### Frederick GothamGuest

sarathy posted:

> Please verify and revert back in case.

*Cringe*

I'd love to bludgeon to death the next person I hear utter that phrase.

--

Frederick Gotham

Frederick Gotham, Aug 1, 2006
10. ### Richard HeathfieldGuest

Frederick Gotham said:

> sarathy posted:
>
>> Please verify and revert back in case.

>
>
> *Cringe*
>
> I'd love to bludgeon to death the next person I hear utter that phrase.

Are you sure about that? Please verify and revert back in case.

(And now if you'll excuse me, I have a plane to catch. Or a starship. Or
something... TAXI!)

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at above domain (but drop the www, obviously)

Richard Heathfield, Aug 1, 2006
11. ### Frederick GothamGuest

Richard Heathfield posted:

>>> Please verify and revert back in case.

>> *Cringe*
>>
>> I'd love to bludgeon to death the next person I hear utter that phrase.

> Are you sure about that? Please verify and revert back in case.
>
>
>
> (And now if you'll excuse me, I have a plane to catch. Or a starship. Or
> something... TAXI!)

That phrase brings back horrible memories of working in an office full of
social retards. Never again.

--

Frederick Gotham

Frederick Gotham, Aug 1, 2006
12. ### =?iso-8859-1?q?Kirit_S=E6lensminde?=Guest

=?iso-8859-1?q?Kirit_S=E6lensminde?=, Aug 1, 2006
13. ### Ancient_HackerGuest

Roy Smith wrote:
It's pretty much an obsolete concept as far as hardware design goes.

Not quite, many DSP-oriented CPU's use 1's complement arithmetic.

The advantage is, in a chain calculation, the negates and carries can
be computed separately and andded back at the end. With two's
complement the "add one" has to be done on each negate.

Ancient_Hacker, Aug 1, 2006
14. ### Keith ThompsonGuest

"Kirit Sælensminde" <> writes:
> Roy Smith wrote:
>> That being said, I haven't seen a 1's complement
>> machine in a couple of eons. It's pretty much an obsolete concept as far
>> as hardware design goes.

>
> Except of course as part of the format for IEEE floating point numbers
> (float, double etc.).
>

Actually, I think it's sign-and-magnitude, not one's-complement.

--
Keith Thompson (The_Other_Keith) <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

Keith Thompson, Aug 1, 2006
15. ### Dik T. WinterGuest

In article <> "=?iso-8859-1?q?Kirit_S=E6lensminde?=" <> writes:
>
> Roy Smith wrote:
> > That being said, I haven't seen a 1's complement
> > machine in a couple of eons. It's pretty much an obsolete concept as far
> > as hardware design goes.

>
> Except of course as part of the format for IEEE floating point numbers
> (float, double etc.).
>

I would not trust a book by an author who does not know the difference
between 1-s complement and sign-magnitude. The last machine I had
access to that used 1-s complement was the CDC Cyber 750, and the
successor in 750 mode (both for int and for float).
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Dik T. Winter, Aug 2, 2006
16. ### J. J. FarrellGuest

Frederick Gotham wrote:
> sarathy posted:
>
> > Please verify and revert back in case.

>
>
> *Cringe*
>
> I'd love to bludgeon to death the next person I hear utter that phrase.

I've never come across it before; what does it mean? Am I allowed to
revert to any previous condition, or is a particular one implied?

J. J. Farrell, Aug 2, 2006
17. ### Joe WrightGuest

Dik T. Winter wrote:
> In article <> "=?iso-8859-1?q?Kirit_S=E6lensminde?=" <> writes:
> >
> > Roy Smith wrote:
> > > That being said, I haven't seen a 1's complement
> > > machine in a couple of eons. It's pretty much an obsolete concept as far
> > > as hardware design goes.

> >
> > Except of course as part of the format for IEEE floating point numbers
> > (float, double etc.).
> >

>
> I would not trust a book by an author who does not know the difference
> between 1-s complement and sign-magnitude. The last machine I had
> access to that used 1-s complement was the CDC Cyber 750, and the
> successor in 750 mode (both for int and for float).

Nobody doubts there were 1's complement iron, but when? The last CDC
machine I saw was the 160A in 1962 and I have no idea of its arithmetic
mode. In 1963 I learned the Philco 212/2000 system which was 2's
complement. Every machine I've seen since then is 2's complement for
integer arithmetic. That's 43 years. But I haven't seen them all.

What was the last 1's complement machine and when was it last produced?

I have never seen 'signed magnitude' integers on any machine.

Of course, IEEE floating point is signed magnitude. FP is not the issue.

--
Joe Wright
"Everything should be made as simple as possible, but not simpler."
--- Albert Einstein ---

Joe Wright, Aug 2, 2006
18. ### =?iso-8859-1?q?Kirit_S=E6lensminde?=Guest

Keith Thompson wrote:
> Actually, I think it's sign-and-magnitude, not one's-complement.

Whoops. Fair enough.

K

=?iso-8859-1?q?Kirit_S=E6lensminde?=, Aug 2, 2006
19. ### Roy SmithGuest

In article <>,
Joe Wright <> wrote:

> What was the last 1's complement machine and when was it last produced?

Wikipedia (http://en.wikipedia.org/wiki/One's_complement) claims "the
PDP-1 and UNIVAC 1100/2200 series, among many others, used one's-complement
arithmetic."

Roy Smith, Aug 2, 2006
20. ### Richard BosGuest

"J. J. Farrell" <> wrote:

> Frederick Gotham wrote:
> > sarathy posted:
> >
> > > Please verify and revert back in case.

> >
> > *Cringe*
> >
> > I'd love to bludgeon to death the next person I hear utter that phrase.

>
> I've never come across it before; what does it mean?

It's managementspeak. The presence of any meaning is purely optional.

Richard

Richard Bos, Aug 2, 2006