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.

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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