A continuous data signal is quantized and transmitted using a PCM system. If each data sample at t UH$17$ he receiving end of the system must be known to within $0\mathrm{.}25\%$ of the peak$-$to$-$peak full$-$scale value $($i$.$e: quantization error$=0\mathrm{.}25\%$ of the peak$-$to$-$peak full$-$scale value$),$ how many binary symbols must each transmitted digital word contain? Assume that the message signal is speech and has a bandwidth of $4$ kHz$.$ Estimate the minimum bandwidth of the resulting PCM signal.