The technical definition of "binary," as provided by Wikipedia, is "composed of two parts or two pieces. It contrasts with Unary, Ternary, Quaternary, and so on." Dictionary.com refers to binary as "consisting of, indicating, or involving two."
I believe you are confusing the simple term "binary" with the "binary number system", which, in its most common form, uses only ones and zeros to form numbers.
Technically speaking, a binary serial number is equivalent to a two-digit serial number, as it consists of two separate digits. These two digits can be any digit spanning 0 through 9, thus meaning that even 3883833 would be a "binary serial number."
Binary serial numbers containing only zeros and ones may be considered a subtype of all binary serial numbers, and I can see how they are somewhat more attractive as they are in the much more commonly seen format of binary numbers.
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