1's complement and 2's complement

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

  1. sarathy

    sarathy Guest

    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 ?

    Please clarify,

    Regards,
    Sarathy
     
    sarathy, Aug 1, 2006
    #1
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  2. sarathy

    SM Ryan Guest

    # 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, Aug 1, 2006
    #2
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  3. sarathy

    red floyd Guest

    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
    #3
  4. sarathy

    Roy Smith Guest

    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.
    Not really
    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
    #4
  5. sarathy

    Bill Pursell Guest

     
    Bill Pursell, Aug 1, 2006
    #5
  6. sarathy

    Michael Mair Guest

     
    Michael Mair, Aug 1, 2006
    #6
  7. sarathy

    sarathy Guest

    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

     
    sarathy, Aug 1, 2006
    #7
  8. sarathy

    Bill Pursell Guest

     
    Bill Pursell, Aug 1, 2006
    #8
  9. sarathy posted:

    *Cringe*

    I'd love to bludgeon to death the next person I hear utter that phrase.
     
    Frederick Gotham, Aug 1, 2006
    #9
  10. Frederick Gotham said:
    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, Aug 1, 2006
    #10
  11. Richard Heathfield posted:

    That phrase brings back horrible memories of working in an office full of
    social retards. Never again.
     
    Frederick Gotham, Aug 1, 2006
    #11
  12. =?iso-8859-1?q?Kirit_S=E6lensminde?=, Aug 1, 2006
    #12
  13. 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
    #13
  14. Keith Thompson, Aug 1, 2006
    #14
  15. Dik T. Winter, Aug 2, 2006
    #15
  16. 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
    #16
  17. sarathy

    Joe Wright Guest

    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, Aug 2, 2006
    #17
  18. Whoops. Fair enough.


    K
     
    =?iso-8859-1?q?Kirit_S=E6lensminde?=, Aug 2, 2006
    #18
  19. sarathy

    Roy Smith Guest

    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
    #19
  20. sarathy

    Richard Bos Guest

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

    Richard
     
    Richard Bos, Aug 2, 2006
    #20
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