Question

Using the same universal set as in the last problem, find the set specified by each of these bit strings.

a) \(1111001111\)

b) \(0101111000\)

c) \(1000000001\)

Short answer

Given: \(U = \{ 1,2,3,4,5,6,7,8,9,10\} \)

If the \(ith\)bit in the string is a \(1\), then \(i\)is in the set.

If the \(ith\)bit in the string is a \(0\), then \(i\)is NOT in the set.

Step-by-step solution

Step 1

(a) The string \(1111001111\) contains a \(1\) for the \(1st,2nd,3rd,4th,7th,8th,9th,\)and \(10th\)bit.

The set then contains the elements \(1,2,3,4,7,8,9,\)and \(10\)

\(\{ 1,2,3,4,7,8,9,10\} \)

Step 2

(b) The string \(0101111000\) contains a \(1\) for the \(2nd,4th,5th,6th,\)and \(7th\) bit.

The set then contains the elements \(2,4,5,6,\)and \(7\)

\(\{ 2,4,5,6,7\} \)

Step 3

c) The string \(1000000001\) contains a \(1\) for the first and tenth bit.

The set then contains the elements\(1\)and \(10\)

\(\{ 1,10\} \)

Thus, we conclude that

a) \(\{ 1,2,3,4,7,8,9,10\} \)

b) \(\{ 2,4,5,6,7\} \)

c) \(\{ 1,10\} \)