Of course the "computer" has no idea what the data "means". Meaning is conceptual. The computing device is mechanical, even though there are no moving parts like in a lawn mower engine.
However, there is a major conceptual aspect to computing. It is common to say that computers either accomplish goals or at least aid in the accomplishment of goals. Goals are purely conceptual. There is no physical entity that is a goal. Likewise, a condition in which a goal is accomplished is also conceptual. In fact everything that can be seen on a computer screen, such as text, graphics, and other user interface objects are conceptual in nature. What is seen is only meaningful within some predefined conceptual context. Text may come in the form of Latin characters strung together to form English words. Graphics may depict conceptual or physical objects or systems.
This is comparable to text or graphics in a book. The book is a physical system, the information itself, taken as a whole, forms a conceptual system. Also, each word, statement and collection of statements, is a conceptual object and system (depending on how it is interpreted).
There is also the concept of a virtual computer, which is a computer where the "hardware" is completely simulated through the software of the (physical) host machine which is it stored on. For example, you can have a physical computer running Linux which contains a virtual computer running Windows. [continues]
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