Writing a custom base64 encoding function in perl

Question

I'm trying to learn perl by writing a custom base64 encoding function, unfortunately I've had no success by now. What I've come to is the following, which doesn't work and I unfortunately don't have any clue about how to proceed.

sub base64($) {
  # Split string into single bits
  my $bitstring = unpack("B*", $_[0]);
  # Pack bits in pieces of six bits at a time
  my @splitsixs = unpack("(A6)*", $bitstring);
  my @enc = ("A".."Z", "a".."z", "0".."9", "+", "/");
  # For each piece of six bits, convert them to integer, and take the corresponding place in @enc.
  my @s = map { $enc[pack("B6", $_)] } @splitsixs;
  join "", @s;
}

Can someone explain to me what am I doing wrong in this conversion? (Please leave aside for now the fact that I'm not considering padding)