Q:

Second Gym: Misty! Who's this Pokemon?

This question is the second one in a series of Poke-related questions I hope that I can ask.
Who's this Pokemon that:

Is is in the first N pokemon, where N is a number most closely to a
power-of-two.
Made Misty freak out.
Made Ash cry.
Can make the best Pokemon of Misty suffer.
Has as a pokedex number, the number that comes after subtracting the
pokedex number of one of the most popular Pokemon of Misty, from a
number that is found in a popular encoding technique in Computer
Science.

As with every Gym you would challenge, all the members (list items) of the Gym Leader (OP) must be defeated (answered) to get the badge (your answer accepted).

A:

It's

 Caterpie

Clue 1

 It's in the first 251 Pokémon, this number being the same as the one established in the first gym, as a byte with all 1s is a power of two minus one and the counts aren't close enough for this difference to matter.

Clue 2

 Yes, yes it did... Misty is afraid of Bug Pokémon.

Clue 3

 Bye-Bye Butterfree is an episode in which Ash's Butterfree (formerly Caterpie) leaves to live with another Butterfree making Ash (and plenty of other children, myself and OP included) cry... also, just gonna drop this little factoid here....

Clue 4

 Misty's best Pokémon (in some of the games, at least; definitely not in the anime) is Starmie, a Water/Psychic type. Caterpie's evolutionary line is Bug type (Butterfree is also Flying, but this does not matter), which is super effective against Psychic and normally effective against Water, thus meaning Bug moves are super effective against Starmie. Though considering base stats this point is debatable.

Clue 5

 Psyduck is one of Misty's most (in)famous Pokémon. Psyduck, being #054, is "ten less" than 64, a power of two (and thus related to binary in a sense), so we seek Pokémon #010 - Caterpie

