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Adding Signed Hexadecimal numbers

  1. Oct 15, 2013 #1
    [Mentor's note: This post does not use the template because it was originally posted in a non-homework forum. I moved it here instead of deleting it and asking the poster to re-post, because he has already shown a reasonable amount of effort.]

    I am having a bit of trouble with this homework assignment...

    I am given two hexadecimal numbers.
    A = 0D34
    B = DD17

    The directions are to find the sum of A and B if they represent signed 16-bit hexadecimal numbers stored in sign-magnitude format.

    I attempted to convert both numbers to binary.

    0D34 = 0000 1101 0011 0100
    DD17 = 1101 1101 0001 0111

    then, because the leading 1 in the binary representation of DD17 makes it negative, I took the 2's comp of DD17 and got 0010 0010 1110 1001.

    However when I add that result with the binary representation of 0D34 I get..

    0000 1101 0011 0100
    + 0010 0010 1110 1001
    --------------------------------
    0011 0000 0001 1101

    which is represented in hexadecimal as 301D. I know this is wrong because the correct answer is CFE3.

    Can anyone point out what I am doing wrong here? It would be of great help.
    Thanks.
     
    Last edited by a moderator: Oct 16, 2013
  2. jcsd
  3. Oct 16, 2013 #2

    CWatters

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    Science Advisor
    Homework Helper

    I believe the rules for signed addition are...

    If they have the same sign, add the magnitudes and keep that sign.

    If they have different signs, then subtract the smaller magnitude
    from the larger one. The sign of the number with the larger
    magnitude is the sign of the result.

    It appears the second case applies because |B| > |A|.

    Edit: Yes that gives the answer CFE3
     
    Last edited: Oct 16, 2013
  4. Mar 20, 2017 #3
    Note that you got the two's complement of the required answer (CFE3) as you subtracted B from A , not A from B.
     
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