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Many 32 bit microcontrollers these days are ARM based. More specifically, they are part of the Cortex-M family.
The Cortex-M0 is the base line of Cortex-M microcontrollers. They are based on the Armv6-M architecture.
The Cortex-M3 is the first of the Cortex-M series. They are based on the Armv7-M architecture.
The Cortex-M4 is an extension of the Cortex-M3. Additional to the instructions available in the Cortex-M3, the Cortex-M4 has some additional DSP instructions. Furthermore, he Cortex-M4 offers an optional FPU. A Cortex-M4 with FPU is also referred to as Cortex-M4F.