It is important to know phase offsets of a binary code in the field of mobile communications because different phase offsets of the same code are used to distinguish signals received at a mobile station from those of different base stations. When the period of the code is not very long, the relative phase offset between the code and its shifted code can be found by counting the number of bits delayed from the code of the same bit streams. But as the period of the code increases, it becomes difficult to find the phase offset. This paper proposes a new method to calculate the phase offset of a binary code. We define an accumulator function, which is used to calculate the phase offsets between the code and its shifted code. Also the properties of the accumulator function are investigated. This number theoretical approach and its results show that this method is very easy for the phase offset calculation. Its application to the code division multiple access (CDMA) system to define a reference code is given. The simple circuit realization of the accumulator function to calculate the phase offset between the received code and receiver stored replica code is described.