Which of the following variable length code word sets is a prefix code (meaning that no code word is a prefix of another code word)?Question 7Select one:{ 1010, 1001, 1011, 01001, 10010, 10101 }{ 0, 10, 110, 1110, 1111 }{ 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, 100, 101, 110, 111 }{ 0, 10, 101, 110, 100 }

Q1. As discussed in the first assignment, it can be helpful to study the probability oferrors and therefore it is useful to know the cardinalities of sets of words and validcodewords — this is where combinatorics comes in.(a) In Question 3 of Assignment 1, it was stated that the set of all bit strings oflength four has 16 elements and the set of all bit strings of length 12 has4096. Justify these cardinalities.2 marks(b) Suppose that a code is made up six digits from the range 0–9 (inclusive)and satisfies the rules:• The first three digits must be odd (and non-zero).• No number is repeated in the first five digits.• The sixth digit is the remainder of the sum of the first five digits dividedby 10.i. How many valid codewords are there?4 marksii. What is the probability that a random selected six digit number is a validcodeword?2 marks(c) One common mistake humans make when reading out numbers is transpo-sitions. Transposition is the special case of swapping letters of a word givenby swapping adjacent letters. (In Assignment 1 we mentioned that ISBN-10could detect such errors.)How many distinguishable rearrangements (not just transpositions) of theISBN-10 code0-205-08005-7are there?2 marksTotal: 10 marksPage 3 of 8

Multiple choice(Select 1 out of 4 options, for the question below.)What does the following pseudocode do?BEGINDeclare an array variable called wordDeclare a conterStore a string in the array wordFOR counter=(length of the word)-1to0counter=counter - 1print word[counter]END FOREND

Find the Hamming distance of the codewords 10100111 and 11010011

29. Let the message word = 0  1  1  1.  Use Hamming (4,7) to form the codeword.Group of answer choices0 1 1 1 1 000 1 1 1 0 1 00 1 1 1 1 0 10 1 1 1 0 0 1

Three of these four words are given in code.The codes are not written in the same order as the words and one code is missing.Find the word for the code 7349.ROCKCAREEARNREAR037809109104