After the 1920, the expression of calculating machine referred to any machine that has made the work of a computer and humans, particularly those who, in accordance with effective methods of the Church-Turing thesis. The thesis States that a mathematical method is effective if it could be defined as a list of instructions can be followed by a man committed within a pen and paper, for as long as necessary and without ingenuity or insight.

Machines that continuously calculated values has become known as analog. They used machines which accounted continues digital quantities, as the angle of rotation of a tree or electric potential difference.

Digital machines, unlike analog, were able to make a state of a numerical value and store each number. Digital machines used different engines or relay before the invention of memory devices faster.

The formula for calculating machine has gradually shelved after the late 1940, to just computer as the emergence of digital electronic machines has become common. These computers were capable of performing calculations were made by the old man committed.

Since the values stored in digital machines are not linked to physical properties as Analog Devices, a computer logic based on digital equipment, was able to do anything that could be called purely mechanical . Alan Turing, known as the Father of Science, A invented such a logical computer known as the Turing machine, which later evolved into the modern computer. These new computers were also able to perform non-numerical calculations, such as music.

From the moment the process of calculation has been made by man committed, the study of computability began a science by being able to make clear that was not explicit in the ordinary sense more immediate.