Results 1 to 3 of 3

Math Help - binary number arithmetic/2

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    4

    Exclamation binary number arithmetic/2's compliment

    To find out the greatest negative number that can be stored in a 4-bit binary word that uses 2's compliment arithmetic.


    The total number of distinct numbers that can be stored in a 4-bit word are 2^4 (including zero) = 16.
    But to store negative numbers, these 16 numbers should be such distributed ,so that every positive number has a 2's compliment negative counterpart.But excluding zero there are 15 numbers exclusively.
    15 being an odd number cannot be divided in two groups equally.This is where the problem arises.

    0000
    0001 -> 1111
    0010 -> 1110
    0011 -> 1101
    0100 -> 1100
    0101 -> 1011
    0110 -> 1010
    0111 -> 1001


    Here we can see seven positive numbers ,seven negative numbers and zero.The count is 15.
    The number omitted is '1000'.
    We know that generally, 1000 is considered as -8 and regarded as the greatest negative number that can be stored in a 4-bit word that uses 2's compliment method.

    1000, if 2's complimented, gives back 1000.How can we differentiate between +8 and -8 ?

    Why is it, that 1000 is always taken as -8 and the greatest positive number that can be stored is 7 and not 8?
    And what about the 2's compliment of zero?
    This 4-bit problem can be applied to any number of bits.


    I hope I could state my problem clearly.Waiting for further discussion...
    Thanks in advance.

    Koustav Ghosal
    Last edited by koustav123; July 22nd 2011 at 11:01 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,502
    Thanks
    765

    Re: binary number arithmetic/2's compliment

    Welcome to the forum.

    Quote Originally Posted by koustav123 View Post
    We know that generally, 1000 is considered as -8 and regarded as the greatest negative number that can be stored in a 4-bit word that uses 2's compliment method.
    Strictly speaking, -8 is the least negative number, or the negative number with the greatest absolute value, that can be stored in a 4-bit word.

    1000, if 2's complimented, gives back 1000.How can we differentiate between +8 and -8 ?
    There is no need to differentiate because 8 is not representable in a 4-bit word.

    Why is it, that 1000 is always taken as -8 and the greatest positive number that can be stored is 7 and not 8?
    By definition of the representation. There may be several equivalent starting points, but one is to postulate that the word b_3b_2b_1b_0 represents the number -2^3b_3+2^2b_2+2b_1+b_0.

    And what about the 2's compliment of zero?
    It is 0 and is found using the standard procedure.

    You are probably familiar with the Wkipedia article about two's complement and especially the section about the most negative number. In fact, this article could be given a more rigorous structure from the mathematical viewpoint (but this would probably make it less readable). It would be nice to give a sequence of definitions and theorems that establish connections between equivalent concepts and operations.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2011
    Posts
    4

    Re: binary number arithmetic/2's compliment

    thank you very much.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability that binary number has no consecutive ones
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: December 9th 2011, 08:40 PM
  2. Replies: 2
    Last Post: May 3rd 2011, 03:22 PM
  3. Number of binary Strings Problem
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: May 14th 2010, 07:09 AM
  4. How to invert binary number in schematic?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 3rd 2009, 06:09 PM
  5. Binary Notation<-->Number Converter
    Posted in the Math Software Forum
    Replies: 5
    Last Post: September 1st 2008, 12:31 PM

Search Tags


/mathhelpforum @mathhelpforum