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- Draw a DFA for a machine that accepts binary strings that start with a 0. (For example, the strings 0, 00, 01, 000, 010, 01101, 01110100 are all in the language.)Construct a pushdown automaton which accepts the set of bit strings with 2/3 as many 0 bits as 1 bits. (For example, 10110 should be accepted, since there are three 1s and two 0s, and two is 2/3 of three.)Implement the following error detection and error correction algorithms using C programming for Hamming code. For Hamming codes, flip a bit in the data and implement the algorithm to correct the same on the receiver side.
- Implement the following function F(x,y,z) using a decoder. This function will return 1 if the value is divisible by Four otherwise it will return zero. asap pls.A bit string contains 1's and 0's. How many different bit strings can be constructed given the restriction(s)? Length is 20. Has exactly six 1's in the first half. Has exactly three 1's in the second half.Given an integer say 45, to find the sum of 45 with 8 in binary form (see the figure below), we can use the TM designed in slides 79-90 of the notes "Turing Machines and Equivalent Models I" twice to find the result. A more effective way is to design a TM to do the addition with 8 directly. 1000 101101 A + = ? Such a TM can be designed by extending the TM designed in slides 79-90 of the notes "Turing Machines and Equivalent Models I". The TM has 14 instructions and 6 states: 0, 1, 2, 3, 4, and halt. Six instructions of such a TM have been given in the first and the second tables below. Fill out the remaining blanks in the first and the second tables and also blanks in the third table to show the remaining instructions of the TM (you have to use your own text boxes here)
- Let X. Y and Z be binary strings of same length and X-Xo X1.. X Xa. Y- yo y. y... Ya- and Z- zo Z1... Z..z A bitwise operation on X and Y is defined as f (X. Y)-Z where z- x, & y. The operation is defined as follows. Design a Turing machine T to compute the function f(X. Y). Assume any two characters as separators among the strings X. Y and Z.A bit (meaning binary digit) is 0 or 1. An ordered array of eight bits (such as01101001) is a byte. How many different bytes are there? If you select a byte at random, what is the probability that you select 11000010? What is the probability that you select a byte containing three 1’s and five 0’s?An irreducible polynomial of degree 8 over GF(2) is given as f(x) =x+x+x'+x +1. This can be used to define GF(2)=GF(256) which is frequently used to design a code over the ASCII symbols consisting of 8 bits. We will use the following notation, for a, e GF(2), e ar + a,r+ ar ++ aa +a, (A) Write a computer program of addition and multiplication for all the binary 8-tuples as above and answer to the following questions: (B) Find any member a in GF(256) with the property that a, a², a²̟., a5 are all distinct, Calculate as al28, and a4. ANSWER: ) :a binary 8-tuple ):a binary 8-tuple ):a binary 8-tuple ):a binary 8-tuple a = ( a4 = ( a12 =( ass = ( (C) Calculate the multiplications a a, att . atza, and a al0 using your program in (A). Verify, for example, that a at = al+64 = ats, a*. a1zi - att12- al92 etc. (D) Define a linear function g from GF(256) to itself such that g(x) = x for any x in GF(256). Here, the linearity implies that g preserves two operations of the field. That is, for any…
- Give regular expressions for the i (a) {w : w contains at most two 1s} (b) {w : w contains at least two 1s} (c) {w: every odd position in w is 1} (d) {w : w contains an even number of 0s, orOne way to electrically or optically represent a binary 1 or 0 is to use the transition between a voltage level (for example, going from a state of no voltage to a state of voltage, or vice versa, on a copper cable) or the transition of having light or no light on a fiber-optic cable to represent a binary 1. Similarly, a binary 0 is represented by having no transition in a voltage level or light level from one time period to the next. This approach of representing binary digits is called state transition modulation.Alice wants to send Bob her account number for his dining dollars. Bob’s account number is 24. Bob wants to encrypt her account number using the RSA algorithm scheme as evil Eve wants to steal her money to buy M&Ms. Bob chooses two prime numbers, 23 and 37, and uses them to compute the number m. Bob then computes the number e and the number d by using things he knows about the number m and its relationship to e. Bob sends the number e and the number m to Alice and she uses them to encrypt her number A and obtains the number C. C is the encrypted version of her code. Alice sends the number C to Bob, and then Bob uses the number d to decrypt Alice’s message. Using this information, encrypt and decrypt the message to show that the RSA algorithm works, then in a few words explain what makes the algorithm secure if the key for encrypting is always public.