Binary logic gates are building blocks of computing machines, in particular, electronic computers. One variant is the programable logic gate, also known as the reconfigurable logic gate, in which the logical function implemented can be modified. In this paper, we construct a mechanism to implement a reconfigurable logic gate. This mechanism is based on the concept of programable multistable mechanisms which we introduced in previous work. The application of a programable multistable mechanism is superior to the different bistable mechanisms previously used to implement logic gates since a single mechanism can be used to implement several logic functions. Our reconfigurable logic gates use a novel geometric construction where the geometric data depend on the stability behavior of the mechanism. There are 16 binary logic gates and our construction can theoretically produce nine of these and our physical model produces six logical gates. Input and output of the mechanism are displacement and the mechanisms can be combined serially, i.e., output of a mechanism is an input for another. We show that we can implement NOR and NAND gates, so combinations of our mechanism can express any logical function. The mechanism is therefore theoretically universal, i.e., implement any computation. We give an analytic model of the mechanism based on Euler-Bernoulli beam theory to find the geometric data, then validate it using finite element analysis and experimental demonstration.