yes, I agree. you drew it wrong before, check out my original post: "use a 2 resistor divider to bring the batt voltage down to the 0-Vdd range (under all circumstances) and hook the middle tap to the positive comparator input. divide Vdd using a 15-25 turn trimpot (best if impedance at the tap is similar to the tap of the other divider when trimmed to the right cutoff point) and hook it to the neg input."
the assumption is that:
IN+ > IN- => output is high impedance
IN+ < IN- => output is low
however, this is just an assumption. in the datasheet this is not specified and there are numerous errors. for example, fig 19 and fig 21 both have a triangle oscillator at the left, and they both use the same circuit except for input polarity. needless to say, one of them does not work. fig 20 uses a strange comparator symbol, where the circle (depicting inversion) is drawn on the positive input... yeah, right.
I wouldn't bother to verify the assumption, but if you want to, check out the LM393 datasheet; this is the device the TLC393 tries improve upon.
now that you decided on a particular comparator, I'll tell you the values of the rest of the components soon. I'm sorry I can't do it right now. don't start building until then.
for the actual build, I recommend a perf board (check wikipedia), or dead bug style (wikipedia) and gluing the components with a hot plastic glue gun. you can use small gauge thermoplastic insulators to use resistors directly as interconnects. once you're sure everything works really fine, you can hot-glue it all for sturdiness. use an IC socket if you use a perf board. actually, it's such a simple circuit that you can really build it any way you want.