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A microprocessor design company started by some ex-Motorola designers, shortly after the Intel 8080 and Motorola 6800 appeared, in about 1975. MOS Technology introduced the 650x series, based on the Motorola 6800 design, though they were not exact clones for legal reasons.
The design goal was a low-cost (smaler chip) design, realized by simplifying the decoder stage. There were no instructions with the value xxxxxx11, reducing the 1-of-4 decoder to a single NAND gate. Instructions with the value xxxxxx11 actually executed two instructions in paralell, some of them useful.
The 6501 was pin-compatible with the 6800 for easier market penetration. The 650x-series had an on-chip clock oscillator while the 651x-series had none.
The 6510 was used in the Commodore 64, released September 1981 and MOS made almost all the ICs for Commodore's pocket calculators.
The PET was an idea of the of the 6500 developers. It was completly developed by MOS, but was manufactured and marketed by Commodore. By the time the it was ready for production (and Commodore had cancelled all orders) MOS had been taken over by Rockwell (Commodore's parent company). Just at this time the 6522 (VIA) was finished, but the data sheet for it was not and its developers had left MOS. For years, Rockwell didn't know in detail how the VIA worked.