...
my $bytes = join '', map chr( unpack( 'V', $rand ) % 256 ), 1 .. $N;
my $set = unpack '%32b*', $bytes;
printf "In $N bytes, there are %d ones and %d zeros\n", $set, length( $bytes ) *8 - $set;
__END__

C:\test>rand -M=97 -N=1e5
In 1e5 bytes, there are 401004 ones and 398996 zeros

C:\test>rand -M=97 -N=1e5
In 1e5 bytes, there are 400686 ones and 399314 zeros

C:\test>rand -N=1e6
In 1e6 bytes, there are 4002738 ones and 3997262 zeros

C:\test>rand -N=1e6
In 1e6 bytes, there are 3997975 ones and 4002025 zeros