Binary Translater Question?

I am new to binary (obviously) but am curious when I go on a binary translater search into google and it pops up i encode the binary equivelent for 1 it decodes and tells me the binary would be 00110001 shouldn't it be 00000001 not what i said before or is it somehow split up into nibbles (4 bits) a like 0011 0001 and the 0001 would be equivalent to 1 also if i type in 120 then it turns up as 00110001 00110010 00110000 wouldn't 120 just be 8 bits not 32 binary is confusing me because every where i look it seems people are doing it differently also a side question if a computer is 64 bits that means it can work with 8 bytes at a time does this mean numbers can be part of any of these bytes like a large number being represented by 2+ bytes or can a number or character only be represented by 1 byte so it can only have 2 to the eighth power possibilities so what im saying is could a 64 bit computer calculate 2,8,4,6,3,8,3,7 at a time or would it be possible for a computer to calculate/process a large number like 1212121092039223483 by combining the 64 bits (i hope you understand what im saying