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Here's an excerpt from a book on computer hardware:

Computers don't judge the information they process because they don't really process information. They process symbols represented by electrical signals. People translate information into symbols that computers can process. The process of translation can be long and difficult. You do some of it by typing, and you know how hard that is—translating thoughts into words, then words into keystrokes.

Computers work logically on the symbols. For the computer, these symbols take electronic form. After all, electrical signals are the only things that they can deal with. Some symbols indicate the dragon, for example. They are the data. Other symbols indicate what to do with the data—the logical operations to carry out. All are represented electronically inside the computer.

Engineers figured out ways of shifting much of the translation work from you to the computer. Consequently, most of the processing power of a computer is used to translate information from one form to another, from something compatible with human beings into an electronic form that can be processed by the logic of the computer. Yes, someone has to write logic to make the translation—and that's what computer programming is all about.

I'm a little bit confused as to how do we know when to use the word form as an uncountable noun and when as a countable noun?

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Well, a simple dictionary lookup tells us a lot. Let's have a look at oxford online.

Basically, form as a noun is _always countable, except in the following cases:

-1.2 [MASS NOUN] Style, design, and arrangement in an artistic work as distinct from its content:
these videos are a triumph of form over content

-2. A particular way in which a thing exists or appears:
essays in book form
energy in the form of light

-4. [MASS NOUN] The customary or correct method or procedure:
an excessive concern for legal form and precedent

-7. [MASS NOUN] The state of a sports player or team with regard to their current standard of play:
they are one of the best teams around on current form

-7.2 A person’s mood and state of health:
she seemed to be on good form

-7.3 British INFORMAL A criminal record:
they both had form

The only use that is confusing, because one example uses form as a mass noun, the other as a countable noun, is meaning 2. Of course, that is also the way form is used in your text.

In the first instance in your text, the sentence follow exactly the example given: in book form versus in electronic form. The question is where the article comes from in the second instance.

In the second instance of form in your text, the reference is not to electronic form in a general sense, but it is about a specific shape (form) in which the information is to be presented: a shape that can be processed by computers. The simple transformation into electronic form as mentioned earlier is no longer adequate to describe it, we need now to specify a specific electronic form. We can conclude there are other forms which may be electronic, but can not be processed by a computer.

So when we describe the way in which a thing appears or exists, we only use form as a mass noun when we refer to the general concept described by that way of existence:

Literature usually appears in book form.

But when we talk about a specific instance or type of that way of existence, we use it as a countable noun:

Paper encyclopaedia were not exactly a portable book form.

Note that in the construction in the form of , form is always countable!

  • Also note that in this example, we say "an electronic form" because "form" is modified by a relative clause: "an electronic form that can be processed by the logic of the computer". It sounds odd if we say "electronic form that can be processed by the logic of a computer", because that relative clause is a limiting clause--it specifies a certain kind of electronic form. – tsleyson Aug 21 '14 at 0:56

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