In this paper, we consider the case for adopting a truly 'digital' type of robot, which would evolve between a discrete and finite set of states. We adopt the point of view that the advantages of traditional robotic evolution (over the full range of a continuous domain) are often negated by complexities associated with the continuous world. The types of discrete robots discussed in this paper would keep this unwanted continuous-time 'genie' in a 'box' of discrete 'steps' during its operation. One distinct advantage of this philosophy is that a formal logical analysis can then be applied to the digital robots, since discrete-time models now correctly and completely model the robot behavior. We argue that there are significant benefits to this strategy in numerous cases, especially with respect to fault detection and fault tolerance. However, there are also disadvantages - in order to guarantee digital behavior, constraints on the robot's operations are imposed. Essentially, we gain formality of digital analysis at the expense of precision of continuous movement. Using an analogy to digital electronics, we discuss ways in which the development of digital robots could revolutionize certain aspects of robotics.