in reply to
Merging text file
A newline is a \n, not a \b.
If your files are text files, why are you using a binmode read?
You are opening the same file twice.
About your core problem: if your files have the same number of lines, you could simply use a while loop for example.
while (defined $line1 = <FILE1>)
Then you read a line from the second file the same way, join them, or concatenate them, then write out the resulting $joinedline to a third file. (Which you already opened for writing.)
I'm too lazy to be proud of being impatient.