One of the challenges of designing hardware circuits is representing the data in an efficient way - minimising area and power while maximising clock frequency. There are several ways of representing variables, each with different characteristics, such as the effect arithmetic operations have on the absolute and relative error. In the first part of this thesis, a new method of transforming arithmetic by combining different numerical representations to exploit their advantages is discussed. The problem is formulated as a set of linear equations which are then solved to find the optimal solution. Algorithms that generate sub-optimal solutions are investigated because they take a fraction of the time to run. A new reconfigurable device structure is proposed based on the results presented. In this case, the accuracy of the original application is guaranteed to be met regardless of the input data. In many applications, guaranteeing that a transformed design has at least the same accuracy as the original is not a strong enough constraint. For this reason, the error on the output is guaranteed to be lower than a specified value. In the second part of this thesis, accuracy reduction is investigated with the goal of minimising circuit area. Energy-efficient run-time reconfigurable hardware is automatically created by systematically deactivating parts of the circuit based on the accuracy required. A model to determine the conditions under which reconfiguring the chip, if this is possible, is more energy-efficient than multiplexing is shown. The approach is expanded to general purpose processors; a new computational model - both software and hardware architecture - to reduce the energy of future devices is introduced.