Feedback shift registers (FSR's), used ubiquitously as pseudorandom pattern generators and for signature analysis, are sometimes implemented with inversions between stages to improve their testability and their ability to locate faults. These intrainverted FSR's (IFSR's) are also attractive because they can be realized with less overhead than standard linear feedback shift registers (LFSR's). This paper shows how to relate the cyclic behavior of the LFSR and the corresponding IFSR, based on the same feedback polynomial, so that IFSR's can be designed to exploit the inherent implementation advantages while exhibiting the well-known behavior of LFSR's. In particular, we show that the cyclic and serial output behavior of LFSR's can be emulated by IFSR's when loaded with the appropriate initial states for most feedback shift register lengths and feedback polynomials. We describe how the initial state for the IFSR can be derived given the feedback polynomial and the initial state of the desired cycle in the LFSR. We also present conditions under which such mapping of behavior cannot be guaranteed.