The original sinclair ZX81 has only a 1kb memory of RAM, so it was quite difficult , but not impossible , to produce any big program, obviously soon there was memory expansion for them and one of those modules was the 16Kb memory extension (usually any image of this blog , compressed and so on it's too big to fit in those memory modules, but in a few years ago 16 kytes of RAM where a lot of space .
As a curiosity , the three first models of sinclair used the same processor, the zilog z80, so where able to access up to 64Kb of RAM (2^16) , so with the different size in their ROM size (BASIC interpreter, Input/Output routines, etc), produces that the total RAM size of the machines where bigger in the first models (up to 60Kb in the sinclair ZX80, 56 kb in the sinclair ZX81 and only 48Kb in the last model sinclair Spectrum.
After the sinclair spectrum the other models (sinclair spectrum 128, +2, and +3 ) used a technique named "pagination" to share a memory space between different memory banks allowing to have more than 64kb, but not at the same time.
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