This problem concerns wind measurements made by the wireless weather station in Example $1-1.$ The wind direction is to be measured with a disk encoder like the one shown in Figure $1-6($ b$).($a$)$ Assuming that the code $000$ corresponds to N list the Gray code values for each of the directions $,$ E W NW NE SW and SE $.($ b$)$ Explain why the Gray code you have assigned avoids the reporting of major errors in wind direction $.$