Counting Bit Strings and Weights

The video tutorial explores the calculation of 10-bit binary strings under various conditions. It begins by determining the number of strings starting with '001', then moves on to calculate strings with a weight of 5 starting with '001'. The tutorial further examines strings that either start with '001' or end with '1101', addressing overlaps using union cardinality. Finally, it calculates strings with a weight of 7 that either start with '101' or end with '01', again considering overlaps. The tutorial uses combinatorial methods to solve these problems.

How many 10-bit strings start with the substring '001'?

• 128

• 64

• 512

• 256

What is the weight of the substring '001'?

• 2

• 1

• 0

• 3

How many 7-bit strings with a weight of 4 can be formed?

• 21

• 28

• 35

• 42

What principle is used to calculate the number of 10-bit strings that either start with '001' or end with '1101'?

• Permutation Principle

• Inclusion-Exclusion Principle

• Pigeonhole Principle

• Binomial Theorem

How many 10-bit strings either start with '001' or end with '1101'?

• 128

• 164

• 200

• 184

What is the weight of the substring '101'?

• 1

• 2

• 3

• 4

How many 7-bit strings with a weight of 5 can be formed?

• 31

• 21

• 16

• 26

How many 8-bit strings with a weight of 6 can be formed?

• 36

• 28

• 32

• 40

How many 5-bit strings with a weight of 4 can be formed?

• 5

• 10

• 20

• 15

How many 10-bit strings have a weight of 7 and either start with '101' or end with '01'?

• 34

• 49

• 39

• 44