I'm not sure what you're asking?
The schematic does look odd.
If you're using a micro then why do you need all of those logic gates?
You do know that you can use diodes to make an AND gate?
To save ICs I'd probably replace the ANDs with diodes and resistors, the NAND can be made from two diodes, a resistor and a NOT gate, then the only IC you'll need is a hex inverter.
**broken link removed**
If you must use AND gates then go for a triple three input AND such as the CD4073 and make the NAND from a NOT gate and a three input AND with one of the inputs permanently connected high.
Still, I think non-inverting logic gates are not needed often because they can easily be substituted with diodes and resistors, most of the time.