What is a byte? Let's assume the modern eight bits.
What is the representation? What other values have to be possible in that representation?
Suppose we assume a pure binary representation which can handle all of the integers from 0 to 65535. In this representation, 65535 is represented by 16 bits: 1111111111111111. This requires two eight-bit bytes.
If the requirement is to have a representation that only handles the two values { 0, 65535 }, or any other choice of two numbers or symbols, we can encode that in as little as one bit: a fraction of a byte.