This project describes the generation of sine waves by a simple recursive digital filter in a way that only 8 bit shift/add/subtraction operations, two permanently occupied 8 bit registers and no data tables are required, therefore permitting the usage of low-cost micro-controllers without multiplication units and little storage capacity. It contains the complete theory of this approach, the finding of suitable parameters under the constraint of 8 bit operations plus substitution of multiplications by shift operations and an example implementation on an ATtiny45 MCU.