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12 April, 14:06

Let A be the set represented by the bitstring 01011011100, let B be the set represented by the bitstring 10110111010. Find the bitstrings representing A c, A ∪B, A ∩B, and A - B.

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  1. 12 April, 16:02
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    Ac = 10100100011

    A U B = 11111111110

    A ∩ B = 00010011000

    A - B = 00010010110

    Explanation:

    Given:

    A = 01011011100

    B = 10110111010

    1) Inverting the bits of A to calculate the complement, Ac = 10100100011

    2) Bitwise union reference:

    0 U 0 = 0

    0 U 1 = 1

    1 U 0 = 1

    1 U 1 = 1

    => A U B = 01011011100 U 10110111010 = 11111111110

    3) Bitwise interselection reference:

    0 ∩ 0 = 0

    0 ∩ 1 = 0

    1 ∩ 0 = 0

    1 ∩ 1 = 1

    A ∩ B = 00010011000

    4) Converting A and B to decimal and subtracting:

    A - B = 732-582 = 150

    Converting 150 to binary, A - B = 00010010110
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