This paper presents an MDD that has additional null-value and all-value edges. The MDD is based on a multi-valued algebra that augments multi-valued variables to allow a null-output value. A null-output value is a value that cannot be computed but represents the lack of any valid value for a given input combination (akin to an output don't care, but its value cannot be changed). A side effect of the null-value edge is that the MDD is capable of representing 1-valued variables. Plus, the null-value is used in representing mutexes (a concept that defines an input don't care condition). While there have been publications that have created BDDs with a third (all-value) edge, to the authors' knowledge, this is the first time an all-value edge has been added to an MDD. This MDD data structure is the foundation for Intrinsity's multi-valued logic synthesis algorithms.