Consider the binary strings consisting of 10 bits
(a) How many contain fewer 1's than 0's
(b) How many contain 5 or more consecutive 1's
(c) How many contain 5 or more consecutive 0's
(d) How many contain 5 or more consecutive 0's OR 5 or more consecutive 1's
Consider the binary strings consisting of 10 bits (a) How many contain fewer 1's than 0's...
1. Consider all the unsigned binary numbers with fewer than 14 bits. a) How many unique numbers are possible? b) How many of these values have the same number of 1's to the left and right of a single 0 (disregarding leading zeros). c) Are any of these numbers prime?
Prob.4 A digital transmission system sends strings of binary (0 or 1) bits through the channel to the receiver. Assume that the probability of a bit error in the channel is 10-2 and that a string of 1000 bits is transmitted (a) Calculate the probability that more than three bit errors will occur in the 1000 transmissions (b) Use the Poisson approximation to calculate the probability that more than three bit errors wil occur in the 1000 transmissions.
Prob.4 A...
Problem 3 (Counting binary strings) 20 marks/ Consider all bit strings of length 15. 1. How many begin with 00? 2. How many begin with 00 and end with 11? 3. How many begin with 00 or end with 10? 4. How many have exactly ten 1's? 5. How many have exactly ten 1's such as none of these 1's are adjacent to each other? Provide detailed justifications for your answers.
Problem 3 (Counting binary strings) 20 marks/ Consider all...
Design a non-ambiguous grammar generating the language consisting of all binary strings, which contain an odd number of 0’s and an odd number of 1’s. Justify correctness of your construction.
Imprecise Counting - Long Runs in Binary Strings Let n=2^k for some positive integer k and consider the set Sn of all n-bit binary strings. Let c be an integer in {0,…,n−k}. Consider any j∈{1,…,n−k−c+1}. How many strings b1,…,bn∈Sn have bj,bj+1,…,bj+k+c−1=00…0? In other words, how many strings in Sn have k+c consecutive zeros beginning at position j? For each j∈{1,…,n−k+c+1}, let Xj be the subset of Sn consisting only of the strings counted in the previous question. Show that (n−k−c+1)∑(j=1)...
Let A be the set of all bit strings of length 10. 1. How many bit strings of length 10 are there? How many bit strings of length 10 begin with 1101? How many bit strings of length 10 have exactly six 0's? How many bit strings of length 10 have equal numbers of O's and 1's? How many bit strings of length 10 have more O's than 1's? a. b. c. d. e.
Exercise 8.12.20: Counting binary strings. (a) How many binary strings of length 12 do not have exactly four 1's? (b) How many binary strings of length 12 start with 101 or 1110? (e) How many binary strings of length 12 start with 00 or end with 00 or both?
4. [6 marks] (Basic Counting) How many bit strings of length 10 contain either five consecutive 0s or five consecutive 1s?
Design a CFG for the strings over {0,1} which contain more 1’s than 0’s. Hint: Draw possible “hill/valley” plots. Dissect each segment you see into simpler structures you’ve seen before. Design a CFG for each, and then piece them together.
animali 32. How many strings of six lowercase letters from the En- glish alphabet contain IS a) the letter a? b) the letters a and b? Osadno-o lls i d c) the letters a and b in consecutive positions with a preceding b, with all the letters distinct?) d) the letters a and b, where a is somewhere to the left of b in the string, with all the letters distinct? into