Question

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.

Answer 1

Ac = 10100100011

A U B = 11111111110

A ∩ B = 00010011000

A - B = 00010010110

Step-by-step 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