Length-Value encoding

Question

I have a homework question. I do not understand the example given. Because how can a byte be 255 bytes? I thought that, because of this example, the answer to (a) is 510 bytes, and the answer of (b) is 128. But yeah, i am confused.. Can someone maybe explain this one?

An alternative encoding scheme is Length-Value encoding, where each string is encoded as a sequence of two elements:  L: a fixed length value that specifies the length of the string in bytes  V: the string itself The length of L, however, limits the maximum length of V. For example if L is a byte V cannot be longer than 255 bytes. Knowing this limitation, how many values can be injectively encoded using LV encoding (a) if the length is encoded using 2 bytes? (b) if the length is encoded using Length-Value encoding with length of 4 bits?

Answer 1

It is not saying that a byte is 255 bytes. It is saying that V (the string being encoded) cannot be longer than 255 bytes, if its length (L) is specified by a single byte 2^8 (0-255). If you used more two bytes you would be able to specify strings up to 2^16 (0-65535) characters long.

For example, if we wanted to encode the value Example. We would write its length (L) and then the value (V). I.e. we would write 7 as a byte followed by the bytes for the ASCII values of the characters in the word 'E', 'x', 'a', 'm', 'p', 'l', 'e'. If we only use a byte for the length then we cannot encode a very long string because a byte's range is 0-255 or 1-256 (256 = 2^8) because a byte only contains 8 bits.

The answers it wants are (a) (2^16 - 1) = 65535 and (b) (2^4 - 1) = 15.

However, the question is mistaken that the maximum length is 255. It should be 256, unless you want to be able to specify zero length strings.