I have been researching Combinatorial Game Theory. One common theme is the assignment of values to games in order to classify the game as a win for a specific player. One such way is class of surreal numbers which is essentially defined as an ordered pair of surreal numbers. 

However, the surreal numbers are mostly useful for analyzing partizan games. For impartial games, the values are fuzzy surreal numbers. Consequentially, in the analysis of impartial games, the concept of nimbers and Sprague-Grundy Values are used. Nimbers essentially relate a position in a normal impartial game to a nim heap. 

My question is that can the nimbers be interpreted in the concept of surreal numbers. For example, the surreal number $* = \{0|0\}$ corresponds to a Sprague-Grundy Value of $0$. Can this approach be extended to all Sprague-Grundy values in such a way that the bitwise xor definition of nimber addition coincides the surreal number addition?