Computable Numbers And The Turing Machine

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Computable numbers.
Abstract
In this essay, the I will express my view on the concept of computable numbers and the Turing Machine that revolutionised the computer science. The essay will explore some basic ideas about computable numbers and show an understanding of whether all real numbers are computable or if only some are computable.
A computable number can be any real finite number that can be approximated by a finite algorithm using a Turing machine. This idea was introduced by Alan Turing in 1936, in his paper “on computable numbers, with the application to Entscheidungs problem”. His concept was rather explicit that he wanted to make the process of enumerating and calculation simple, so he envisioned a different method of calculating and problem solving using logical instructions, such as an algorithm that can be programmed in to a …show more content…

If the desire is to achieve perpetual movement the instruction would have be altered. A new state must be submitted in to the program that allows the machine to move in to and continue the process. This is called “the Machine State”, “After every instruction, we also specify a state for the machine to transition to. In the example, the machine is redirected back to its original state, State 0, to repeat the read-write-nove sequence, unless a blank symbol is read. When the machine reads a blank symbol, the machine is directed to a stop state and the program terminates.” (Cl.cam.ac.uk,

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