For those trying not to go quite so totally geek, a slightly less extreme clock might be something along the lines of:

#!/usr/bin/perl -w

use strict;

$| = 1;

# Set $nice_to_nongeeks true 
#   to use dual-format display 
#   for those not yet fluent in binary.
my $nice_to_nongeeks = 1;

while (1) {
    my @time_components = localtime(time);
    my $datestring      = "The current time is: "
      . join ( ':',
        unpack( "B*", pack( "C", $time_components[2] ) ),
        unpack( "B*", pack( "C", $time_components[1] ) ),
        unpack( "B*", pack( "C", $time_components[0] ) ) );
    if ($nice_to_nongeeks) {
        $datestring .= ' ('
          . join ( ':',
            substr('00' . $time_components[2], -2),
            substr('00' . $time_components[1], -2),
            substr('00' . $time_components[0], -2) )
          . ')';
    }

    # Append to the string its length in backspace 
    #   characters so as to overwrite its previous output.
    # (There may perhaps be some terminals where 
    #   this might not work, however.)
    $datestring .= "\b" x length($datestring);
    print($datestring);
    sleep(1);
}
[download]

(I thought the idea of a binary clock was cool, but didn't like represent-each-digit-as-binary approach, thinking the represent-each-component-as-binary was a little more true to the idea.)

Enjoy.

Update: Modified code to force time components in dual-display mode to 2 digits.