We present three methods of weighting N-bit wlaw Pulse Code Modulation (PCM) with binary modulation, and evaluate their performances theoretically for transmission over Rayleigh fading and Gaussian channels. The digital modulation methods considered are noncoherent frequency shift keying and coherent phase shift keying. Ideal selection combining and ideal maximal ratio combining diversity techniques are employed when the transmission is over fading channels. Weighting System 1 is the conventional weighted pulse code modulated system, where the bits in every PCM word have the same weighting profile. Weighting System 2 has 2 N unique weighting profiles, while System 3 has an addendum to System 2, where every bit in a particular word is further weighted by a unique multiplicative factor. For Rayleigh fading channels and the encoder operating at an input level that provided maximum signalto-quantization noise-ratio, we obtained gains in overall signal-to-noise ratio (sin) over unweighted Il-Iaw PCM of 3, 4.5, and 6 dB for Systems 1, 2, and 3, respectively. When the systems were used in conjunction with Gaussian channels, the corresponding gains were 10, 12, and 17 dB, for a channel sin of 10 dB. In addition to the theoretical results, we conducted computer simulations using four concatenated speech sentences transmitted via our weighted wlaw PCM systems over mobile radio channels. The simulation performances were in good agreement with our theoretical results, which were based on input signals having an exponential distribution.