A1024-bit message is sent that contains 992 data bits and 32 crc bits. crc is computed using the ieee 802 standardized, 32-degree crc polynomial. for each of the following, explain whether the errors during message transmission will be detected by the receiver: (a) there was a single-bit error. (b) there were two isolated bit errors. (c) there were 18 isolated bit errors. (d) there were 47 isolated bit errors. (e) there was a 24-bit long burst error. (f) there was a 35-bit long burst error.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?