MATH SOLVE

4 months ago

Q:
# Let A be the set represented by the bitstring 01011011100, let B be the set represented by the bitstring 10110111010. Find the bitstrings representing Ac, AUB, AnB, and A-E.

Accepted Solution

A:

Answer:Ac = 10100100011[tex]A \cup B = 11111111110[/tex][tex]A \cap B = 00010011000[/tex][tex]A - B = 100100111010[/tex]Step-by-step explanation:All these operations are bitwise operations.Ac is the complement of a. So where we have a bit 0, the complement is 1. Where we have a bit 1, the complement is 0. SoA = 01011011100Ac = 10100100011The second operation is the union between A and B. This is bitwise(bit 1 of A with bit 1 of B, bit 2 of A with bit 2 of B,...). The union operation is only 0 when it is between two zeros. So:A = 01011011100B = 10110111010[tex]A \cup B = 11111111110[/tex]The third operation is the intersection between A and B. Again, bitwise. The intersection is only 1 when it is between two bits that are 1. SoA = 01011110100B = 10110111010[tex]A \cap B = 00010011000[/tex]The last operation is the bitwise subtraction between A and B. We start from the least significant bit(the last one). And we have to take care of the borrow operator also, similarly to a decimal subtraction.We can only borrow from a previous bit 1, and this bit is set to 00-0 is 0 with no borrow1-0 is 1 with no borrow1 with borrow - 0 is 1 with borrow1 with borrow - 1 is 1 with no borrow0-1 is 1 with no borrow0 with borrow -1 is 0 with no borrow1-1 is 0 with no borrowIf we arrive at the first bit(the most significant) with a borrow, we must add a 1 at the front of the answer. SoA = 01011110100B = 10110111010[tex]A - B = 100100111010[/tex]