We are given that we want to be able to resolve the temperat

We are given that we want to be able to resolve the temperature in 1 degree Celsius increments over a range of 0 degrees to 125 degrees Celsius Determine the following: How many codewords are needed to provide an accuracy of 1 degree over the temperature range given Provide the number of bits (N) along with how many unique values that it can attain (X) Show that if you choose N-1 bits there is not enough unique codewords to meet the requirements Suggest an assignment of codewords for each degree over the range 0 to 125 degrees Celsius.

Solution

1)

the temprature range 0 to 125, Total temprature present with this range with 1 degreee celicuis incremnet

0+125+1=126

so we need 126 code words to represent the range between 0to 125 with 1 degreee celicuis incremnet

2)No of Bits N>=Log₂(No of code word)

N>=Log₂(126)

N>=6.9773

so we choose the mini no of integer value for this condition is 7

N=7, is required bit to represent the code word.

It can represent Upto 128(2⁷) code words.

3.if we ch0ose N-1 bits, then 2⁶= 64 code words can be reprsent. so its not cover the range 0to 125

4)

0000000=0celcies

0000001=1celcies

0000010=2celcies

0000011=3celcies

.

..

....

1111100=124celcies

1111101=125celcies