You were recently hired to operate the MSU scoreboard for a variety of sporting

Question

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 2. 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 For MSU disc golf events, each score represents the number of strokes the player is above or below a certain threshold (par). Disc gotf 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 b. how you would represent a score of -35' using UP/DOWN notation. How many unique scores can be generated if you are required to use 11 switches? c.

Explanation / Answer

Answer is as follows :

a)

As per given information ,, the score never exceeds 160.

so let us take binary equivalent of 160 i.e.10100000 i.e. of 8 bits.

So minimum 8 number of switches need to represent any score on board with given range.

As lowest score you could represent with 8 bit swithces is 00000000 i.e. equal to 0.

So lowest score is 0.

As highest score you could represent with 8 bit swithces is 11111111 i.e. equal to 255.

So highest score represent is 255.

for 92 we know that 01011100 is 8 bit binary number of 92.

So it is represent with

UP DOWN UP DOWN DOWN DOWN UP UP.

b)

For given scenario we know that 27 is equal ot 11011(5 bits) and one more bit is required at leftmost to indicate the sign. So total of 6 bits are required.

thew lowest score we represnt is 1 11111 where 1 indicate -ve sign, so it is equal to -31.

and highest socre is 0 11111 where 0 indicates +ve sign, so it is equal to +31.

35 is represnt with 100011 in binary, and one more leftmost bit for -ve sign.

So -35 is represent as 1 100011

i.e. equal to

DOWN DOWN UP UP UP DOWN DOWN.

c)

For this we have 11 bits so

it vary from 00000000000 to 11111111111 i.e. equal to 0 to 2047.

So maximum of 2048(0 to 2047) unique no are generated.

You can also calculate it by 211 = 2048.

if there is any query please ask in comments......

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