The behavior of the Five-Phase Twisted-Ring Counter (5P-TRC) circuit is analyzed. The circuit produces five individual phased clock signals that exercise a phase difference equal to the half period of the clock. A tree-like structure is built by applying the phased outputs of the circuit to the clock inputs of five replicas of the circuit in order to extend its behavior. The EXOR5 gate is used to define a mirroring structure attached to the 5P-TRC structure such that a primitive/expanded counter configuration is formed. A fundamental concept being described by the transposition mechanism of the EXOR operator is incorporated to the above configuration such that the phase association of interconnecting signals is preserved.