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I don't know much about memory. Here are some lines from CLRS:

The words in a computer memory are typically addressed by integers from 0 to $M - 1$, where $M$ is a suitably large integer. In many programming languages, an object occupies a contiguous set of locations in the computer memory. A pointer is simply the address of the first memory location of the object, and we can address other memory locations within the object by adding an offset to the pointer.

Now, what does 'word' mean here? Does it mean a finite sequence of characters from the keyboard? If yes then I know that we can set $M = 256$ so that ASCII would cover all these characters but then the problem is that $M$ wouldn't be that large as it should be and also it should have been said 'letters in a computer memory', not 'words in a computer memory'.

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No, it refers to a word in a computing sense. Here, a word is just a unit of data, whatever is natural for a particular processor. For instance, an x86-64 processor, which I'm currently using, has a word size of 64 bits. So a single word in this case consists of 64 bits.

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