bit strings of a fixed length are needed to form a code. what is the minimum length of the string is one string is needed to represent each letter of the alphabet and each decimal digit?

I am not certain you mean decimal digit, perhaps you mean 0.1.2.3...

you need 36 codes.
one bit gives you 2
two bits gives you 4
three bits give you 8
four bits give you 16
five bits give you 32
six bits give you 64

Now if you need stop, start bits, or checksum,you have to add those.