You can convert binary strings to hexadezimal representation (i.e. text strings) and back using the Perl functions pack() and unpack(). There are a little confusing - I personally have problems to remember which does which way conversation - but very powerful. See perldoc for the details and you will definitely find a tutorial on the web how to use it.

The code should look like this (untested):

open(IN, '<', $ifilename);
binmode(IN);
while (!eof IN) {
  read(IN, my $binstring, $length);
  my $hexstring = unpack("...", $binstring);
}
[...]
my $newbin = pack("...", $hexstring);
[download]

Please note that pack() awaits a list of arguments...

Update:
See this tutorial. Direct at the start it shows how to do bin2hex and hex2bin!

Are you sure you don't actually want a hex editor? You can manipulate binary directly with perl. Hex is just human readable binary and if you plan on programatically manipulating it why bother converting to and from a human readable form? You may find Pack/Unpack Tutorial (aka How the System Stores Data) useful, especially if you have structured binary data.

warn unpack 'H*', 'Hi';
warn pack 'H*', unpack 'H*', 'Hi';
[download]