bit patterns of negtive numbers?

This is a discussion on bit patterns of negtive numbers? within the C Programming forums, part of the General Programming Boards category; hi there: i am just learning more about data types and thought i will write a short code to see ...

  1. #1
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    bit patterns of negtive numbers?

    hi there:

    i am just learning more about data types and thought i will write a short code to see the bit patterns of signed variable, in this case a char.

    i know that the first bit of signed data types is called sign bit, so i suspected to see something like:

    decimal 1 -> 00000001
    decimal -1 -> 10000001

    the left most bit being the sign bit.

    however, in the code i worte i got:

    decimal value -> -1 :: bit pattern -> 11111111
    decimal value -> 1 :: bit pattern -> 00000001

    and it seems that -128 comes after +127 as:

    decimal value -> 127 :: bit pattern -> 01111111
    decimal value -> -128 :: bit pattern -> 10000000

    my question is that, if this is the correct bit representation of signed char, how does negative numbers are convereted into bit patterns? of course, it could be something wrong in the code i wrote, my code are as below:

    main()
    {
    char string[9];
    int i;
    char test;
    unsigned char MASK;

    for(test = -128; test<127; test++)
    {
    MASK = 1<<7;
    for(i=0; i<8; i++)
    {
    sprintf(string+i, "%d", (test & MASK) ? 1 : 0);
    MASK>>=1;
    }
    string[8] = (char)NULL;
    printf("decimal value -> %d :: bit pattern -> %s\n", test, string);
    }
    }

    many thanks

    CHUN

  2. #2
    Registered User hk_mp5kpdw's Avatar
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    Negation is accomplished using something called two's complement. Do a search on it to find out more but basically to convert a value from positive to negative, you negate all the bits (zeros become ones and ones become zeros) and then you add 1. So, if 1 is 00000001 then to negate it we first takes its ones complement which is 11111110 and then add 1 to get the two's complement which is 11111111. 127 is 01111111 so -127 is 10000000 (ones complement) and add 1 to get the final answer of 10000001. -128 is 1 less than -127 so take 10000001 and subtract 1 and you get 10000000.
    Last edited by hk_mp5kpdw; 11-08-2004 at 06:33 AM.
    "Owners of dogs will have noticed that, if you provide them with food and water and shelter and affection, they will think you are god. Whereas owners of cats are compelled to realize that, if you provide them with food and water and shelter and affection, they draw the conclusion that they are gods."
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  3. #3
    & the hat of GPL slaying Thantos's Avatar
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    The reason for the twos complement is so you can add signed numbers and get the correct result.

    1 + -1 = 0

    Code:
     00000001
    +11111111
    ----------
    100000000
    But you only take the least signficant bits (in this case 8) so you get 00000000

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    thanks, i will look into it in more depth.

    cheers

    CHUN

  5. #5
    Just Lurking Dave_Sinkula's Avatar
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    Quote Originally Posted by chunlee
    i am just learning more about data types and thought i will write a short code to see the bit patterns of signed variable, in this case a char.

    i know that the first bit of signed data types is called sign bit, so i suspected to see something like:

    decimal 1 -> 00000001
    decimal -1 -> 10000001
    There are three possible representations of signed integral types in C:
    • sign and magnitude
    • two's complement
    • one's complement
    A brief description is here. Use Google for more.
    Last edited by Dave_Sinkula; 11-08-2004 at 07:27 AM. Reason: i before e except after c
    7. It is easier to write an incorrect program than understand a correct one.
    40. There are two ways to write error-free programs; only the third one works.*

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