1a Consider sampling quantizing digitizing analog temperatur

1.(a) Consider sampling (quantizing, digitizing) analog temperatures. If you want the difference between each digital temperature to be no more than 0.095 degrees and you have 5 bits per sample, what is the largest temperature you can represent if the minimum temperature is 97 °F?

(b) Now consider sampling analog temperatures in the range from -916 to 581 °F. If you use 7 bits per sample, how many degrees F does a single sample bit represent? (In other words how much temperature is represented by going from one binary number to the next?)

Solution

a)

number of bits =

total quantization states that can be represented using these 5-bits = 2⁵ =32

since each state rep[resent a 0.095F raise

therefore total raise =0.095*32=3.04F

minimum temperature = 97F

therefore maximum temperature =97+3.04=100.04F

b)

range of temperatures = -916 to 581

therefore, the difference = 581+916=1497F

availabe bits =7

7 bits can represent 2⁷ =128 states

we ivide total temperature range by the total quantization states to obtain the resoution( degrreF a sampe bit can represent)

= 1497/128=11.69F