MPC is becoming increasingly implemented on embedded systems, where low precision computation is preferred either to reduce costs, speedup execution or reduce power consumption. However, in a low precision implementation, constraint satisfaction cannot be guaranteed. To enforce constraint satisfaction under numerical errors, we adopt tools from forward error analysis to compute an error bound on the output of the embedded controller. We treat this error as a state disturbance and use it to inform the design of a constraint-tightening robust controller. The technique is validated via a practical implementation on an FPGA evaluation board.