if (($value & $mask) == $mask) ...

##</code><code>##

my $mask = 0b00001110;  # test if bits 2,3,4 are set

check($_, $mask) for 0b01101110,
                     0b01100110;

sub check {
    my ($value, $mask) = @_;
    printf " val %08b\n", $value;
    printf "mask %08b\n", $mask;
    print  "   & --------\n";
    printf "     %08b ", $value & $mask;

    if ( ($value & $mask) == $mask ) {  # equals mask?
        print "=> all tested bits set";

    } elsif ( $value & $mask ) {        # just true?
        print "=> some tested bits set";
    }
    print "\n\n";
}

__END__

 val 01101110
mask 00001110
   & --------
     00001110 => all tested bits set

 val 01100110
mask 00001110
   & --------
     00000110 => some tested bits set