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You were recently hired to operate the MSU scoreboard for a variety of sporting events hosted on campus.
2. You were recently hired to operate the MSU scoreboard for a variety of sporting events hosted on campus. Unfortunately, the MSU scoreboard requires that the operator enter in the appropriate score using a series of binary switches where a switch in the UP position denotes a '0' and a switch in the DOWN position denotes a '1' (ex. UP-DOWN-DOWN-UP would be 0110).
a. For MSU football events, the scores are always positive integers that never exceed 160 points. Assuming that all of the switches will be used only to represent digits (no excess bit), what is the minimum number of switches needed to represent any score within this range? What is the lowest score you could represent with this number of switches? What is the highest score you could represent with this number of switches? Describe how you would represent the score '92' using UP/DOWN notation.
b. For MSU disc golf events, each score represents the number of strokes the player is above or below a certain threshold (par). Disc golf scores can be either positive or negative integers that never exceed +/- 27. Assuming that the leftmost switch is reserved as an excess bit and all of the remaining switches represent digits, what is the minimum number of switches needed to represent any disc golf score within this range? What is the lowest score you could represent with this number of switches?
What is the highest score you could represent with this number of switches? Describe how you would represent a score of '-35' using UP/DOWN notation.
c. How many unique scores can be generated if you are required to use 11 switches?
