Another way to shift through the ascii bit pattern is with split. A split on //, separates a string into individual characters.

#!/usr/bin/perl -w
use strict;

my @ltrs = qw (A B C D);
my $num = "0101";

print "$num=>";
my $i =0;
foreach my $bit (split(//,$num))
{
   print $ltrs[$i] if $bit;
   $i++;
}
print "\n";

# prints: 0101=>BD
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I did not get the impression that the OP was interested in doing actual binary to decimal conversion although jwkrahn's suggestion of: $decimal = oct( "0b$input" ); looks like a "winner" to me in the case of ASCII strings.

I would like to hear more about the application if these bits or combinations of bits represent something other than just a number. I probably would have some suggestions in that event, but want to hear more before running off on a tangent.