More Perlish techniques will be welcomed.

I don't mean to rain on your parade, but I think that one of the most Perlish techniques is to see whether anyone else has already written it... enter Math::BaseCalc.

#! /usr/bin/perl -w

use strict;
use Math::BaseCalc;

my $bin = Math::BaseCalc->new( digits => [0,1] );

my $num;
for $num( @ARGV ) {
        print "$num base 2 = ", $bin->from_base($num), " base 10\n";
}
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When run, the above produces:

% ./b2d 1110010101011101111011110110101010111
1110010101011101111011110110101010111 base 2 = 123140435287 base 10
[download]

And you can be sure that the module has received extensive testing...

Update: you're right, if the number to be converted is big enough, it will use scientific notation. You learn something every day.