Give an informal description of a Turing machine with three tapes,that gets as input the binary representation of an arbitrary integer m ≥ 1 , and returns as output the unary representation of m a) Beginning of the calculation: Convert the number m of the first strip in binary. contains. The other 2 strips are empty (containing only the _ symbol). Our Turing machine is in the start state. b) End of calculation: 3rd lane includes conversion of m number in unity basis, i.e. It contains an array of m 1's. Our Turing machine is in the finishing position (final state). c) Hint: You can arrange the 2nd strip to contain 1 as one of the powers of 2.c) Hint: Arrange the order to contain 1' as one of the 2 powers

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.