Write a Turing machine that converts its input from binary to unary. In other words, if the input is the string x ∈ {$, 0, 1}∗ , a $ followed by the binary expansion of the nonnegative integer n (for example, $101 to represent n = 5), then the machine outputs the string 1^n . You may assume the input string will be in this format, i.e., a $ followed by either just a 0, or followed by a binary string beginning with 1.

Java, please solve this nice problem, thanks alot

We are going to write a Turing machine that reads a string of 1's as input and produces a 1 for output if the string is a length that is a multiple of 3 and outputs a O otherwise. The 1 or O should be spaced 1 position to the right of the end of the input. You may assume that the input contains only zero or more 1's. For example here are four before and after snapshots. Before After B1 В Input is zero 1's (0 is a multiple of 3) <== 1 1 0 11 11 0 111 111 1 Here is a Turing machine that does most of the work but is missing one instruction. Fill the blank with the instruction needed. Follow the format of the other instructions (ie, current-state current- head head-instruction new-state, with exactly one space between each). qO 1 R q1 q1 1 R q2 q2 1 R q0 q0 BR q3 q1 BR q4 93 В 1 q5 q4 B0 q6 Hint: I suggest you draw what is given and then figure out what single instruction will make the machine behave as described.

Write a program that takes in a positive integer as input, and outputs a string of 1's and 0's representing the integer in binary. For an integer x, the algorithm is: As long as x is greater than 0 Output x % 2 (remainder is either 0 or 1) x = x / 2 Note: The above algorithm outputs the 0's and 1's in reverse order. Ex: If the input is 6, the output is: 011 (6 in binary is 110; the algorithm outputs the bits in reverse).