my @num = ( "0000", "0101", "1010", "1111" );

my ( $n1, $n2 ) = ( "0", "1" );

my $ndiff = abs( $n2 - $n1 );

for ( my $i = 0 ; $i < @num ; $i++ ) {
    for ( my $j = $i + 1 ; $j < @num ; $j++ ) {

       # Count oriented matches and mismatches along string
        print join(
            "\t",
            $num[$i],
            $num[$j],
            ( ( $num[$i] | $num[$j] )  =~ tr[0][0] ),      #count 00
            ( ( ~$num[$i] & $num[$j] ) =~ tr[\1][\1] ),    #count 01
            ( ( $num[$i] & ~$num[$j] ) =~ tr[\1][\1] ),    #count 10
            ( ( $num[$i] & $num[$j] )  =~ tr[1][1] )       #count 11
          ),
          "\n";

        # Attempt at flexible version via eval
        my ( $string1, $string2 ) = ( $num[$i], $num[$j] );
        print join( "\t",
            $string1,
            $string2,
            ( eval "( $string1 | $string2 )  =~  tr[$n1][$n1]" ),
            ( eval "( ~$string1 & $string2 ) =~ tr[\$ndiff][\$ndiff]" ),
            ( eval "( $string1 & ~$string2 ) =~ tr[\$ndiff][\$ndiff]" ),
            ( eval "( $string1 & $string2 )  =~ tr[$n2][$n2]" ) ),
          "\n\n";
    }
}

__END__
# Output from example
# In each pair of lines, the first is the desired.

0000	0101	2	2	0	0
0000	0101	0	0	0	0

0000	1010	2	2	0	0
0000	1010	2	0	0	0

0000	1111	0	4	0	0
0000	1111	0	0	0	0

0101	1010	0	2	2	0
0101	1010	1	0	0	0

0101	1111	0	2	0	2
0101	1111	0	0	0	0

1010	1111	0	2	0	2
1010	1111	1	0	0	0