My first was a ZX-80, my second was a ZX-81 with 1K memory. My Dad (who worked for ICL at the time) came home one day with a 2K chip, suddenly my horizons were expanded 100%. A few weeks later over a weekend he built me a 16K RAM Pack, giving me 18K RAM ... the limits seemed endless.
Peeking and Poking memory locations was the height of fashion back then :)
>> ...it was actually a Z-80 with 64M RAM...
> I suspect you mean 64k RAM (how soon we forget)
This sketchy description sounds very much like the Osborne 1 or the KayPro 2 (with the the two 5.25" floppies).
It was an interesting time. The OS booted in about 5 seconds, Wordstar took about 20K of memory (using overlays to swap in code), a single floppy could hold the OS, an application, as well as some data.