in the shell

I can't understand a conversation in episode 15 of season 1. A tachikoma is talking to Batou during a live fire exercise for new recruits. The Tachikoma keeps talking about how the major been giving them scaring looks lately and how they've achieved personality.

What I don't understand is the statement about the tachikoma coming to understand the concept of god, and how the concept he's trying to describe is

"different from the concept of zero, there is no way to send the invalid input response when we are told to shut down permanently with no good reason. If that is god in analog, then it's zero in digital, how is that? Well, we're made from advanced digital devices, right? So we've gathered so much information that it can't all be stored in our ghosts. But you analog based people, your ghost isn't damaged no matter how many digital devices are needed to become a cyborg or get a cyberbrain. Furthermore, you can die if you have a ghost. How nice. Anyway, how does it feel to have a ghost?"

This reads like gibberish to me, but I know it has to do with the issues raised by the Tachikomas growing sentience and personality. Can anyone give me the gist of what he's trying to say and its relevance to the above theme?

Yes. that is a rather difficult statement to understand and it doesn't help, that Tachikoma apparently has difficulties to express himself in this complex level.
In some schools of Buddhism, though, God is considered to be the infinite nothingness, which could explain the analogy of "zero". Or it could refer to the fact, that humans can be "told to shut down" - that is, to die - without their own constent by this higher entity and that way defines God via the power to terminate existance.

The latter portion is somewhat easier to understand - Tachikoma is envious of humans who can store far greater amounts of information to their Ghosts that he can have in his databank, yet they suffer no ill effects from adding up to it with cyberbrain-computers, thus in a way having the best from both worlds. As for the comment about death, Tachikoma is a half-immortal AI with no fixed lifespan. Backups can be always taken and resurrected, so under normal circumstances it is impossible for a Tachikoma to experience death. Presumably he is envious to Batou, because Batou is capable of experiencing something that he knows he can't.

Furthermore, this conversation slightly parallels the chat between Batou and Fuchikoma in the original GitS manga. It wasn't nearly as deep, though.

I'm totally new to the forum, so please excuse me if there are disagreements around the various GITS translations that I'm unaware of,

but here's the sub-title version of most of the Tachikoma's dialogue from that scene, as it appears on the DVD I just watched:

"And you know that "existence of God" thing I had trouble understanding before? I think I'm starting to understand it now. Maybe, just maybe, it's a concept that's similar to a zero in mathematics. In other words, it's a symbol that denies the absence of meaning - the meaning that's necessitated by the delineation of one system from another. In analog, that's God. In digital, that's zero."

I think that's a bit clearer and easier to understand than the version you posted above. Pretty metaphysical still, but clearer.