Suppose that the universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Express each of these sets with bit strings, where the ith bit in the string is 1 if i is in the set and 0 otherwise:

a) { 3, 4, 5 }

b) { 1, 3, 6, 10 }

c) { 2, 3, 4, 7, 8, 9 }

Question

Mathematics

Beau Faulkner

10 June, 18:40

Suppose that the universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Express each of these sets with bit strings, where the ith bit in the string is 1 if i is in the set and 0 otherwise:

a) { 3, 4, 5 }

b) { 1, 3, 6, 10 }

c) { 2, 3, 4, 7, 8, 9 }

+4

Answers (1)

Know the Answer?

Mathew · Answer 1

a. 0011100000

b. 1010010001

c. 0111001110

Step-by-step explanation:

We are given that a universal set

U={1,2,3,4,5, ... 10}

We have to express each given set with bit strings, where the ith bit in the string is 1 if i is in the set and 0 otherwise

a.{3,4,5}

For 1=0 because 1 is not in the given set

For 3=1, For 4=2, For 5=1 because 3,4 and 5 are in the set

For 2=0

For 6=0

For 7=0

For 8=0

For 9=0

For 10=0

Therefore, bit string=0011100000

b.{1,3,6,10}

For 1,3,6 and 10 write 1 because these elements are present in the set and for 2,4,5,7,8,9 write 0 because these elements are not present in the set

Bit string = 1010010001

c.{2,3,4,7,8,9}

Similarly

Those elements which are present in the set then for those elements write 1 otherwise 0.

Bit string = 0111001110

Suppose that the universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Express each of these sets with bit strings, where the ith bit in the string is 1 if i is in the set and 0 otherwise:a) { 3, 4, 5 }b) { 1, 3, 6, 10 }c) { 2, 3, 4, 7, 8, 9 }

Suppose that the universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Express each of these sets with bit strings, where the ith bit in the string is 1 if i is in the set and 0 otherwise:

a) { 3, 4, 5 }

b) { 1, 3, 6, 10 }

c) { 2, 3, 4, 7, 8, 9 }