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.

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"Computeri non cogitant, ergo non sunt"