$($b$)$ A $400-$milliwatt signal goes through ten devices, each with a noise level of $12\mathrm{.}65$ microwatts on average. The signal contains frequencies of $1000Hz,2000Hz,3000Hz,$ and $4000Hz.$ Calculate the theoretical highest bit rate for the channel. Suppose, the theoretical maximum bit rate becomes $12000$ bps if the above$-$mentioned channel is noiseless. In this case, what is the number bits per signal level used to represent the data?