Key-indexed search in existence tables
I have a doubt about one of my book's statement.

Talking about key-indexed search in a symbol table, at a certain point it says: "*If there aren't records (but only keys), we can use a bit table. In this case, the symbol table is called existence table, because we can consider the k-th bit as an indicator whether the k key there is or there isn't in the table. For example, using a 313-word table on a 32-bit computer, we can use this method to quickly determine whether a given 4-digit internal telephone number was already assigned.*"

Well, I know what a word is, thus that existence table should be a 10.016-bit table, in that case. But what does it mean? What does that fact of the 4-digit telephone number have to do with it? And so, how you can implement a symbol table with key-indexed search, when the records correspond to the keys?
Key-indexed search in existence tables
===

I have a doubt about one of my book's statement.

Talking about key-indexed search in a symbol table, at a certain point it says: "*If there aren't records (but only keys), we can use a bit table. In this case, the symbol table is called existence table, because we can consider the k-th bit as an indicator whether the k key there is or there isn't in the table. For example, using a 313-word table on a 32-bit computer, we can use this method to quickly determine whether a given 4-digit internal telephone number was already assigned.*"

Well, I know what a word is, thus that existence table should be a 10.016-bit table, in that case. But what does it mean? What does that fact of the 4-digit telephone number have to do with it? And so, how you can implement a symbol table with key-indexed search, when the records correspond to the keys?