An in-depth yet simple analysis is presented for binary direct sequence code division multiple access (DS-CDMA) systems considering a frequency selective Nakagami fading channel and maximal ratio combining (MRC) receiver. The inevitable inter-symbol interference as well as multiple access interference from simultaneous users are modeled elegantly and their characteristic functions (CF) are developed. Utilizing the CFs, the exact bit error probabilities are developed following the CF method of error rate analysis that claims the honor to be the first-to-publish reliable result for such channel and receiver. The CF based exact error rate is less computationally intensive than that can be obtained by traditional methods of approximation. The same method also lets us develop a new simpler approximate error rate. The exact method is utilized to investigate the range of parameters where approximations (existing and the new) would be accurate.