Question

Assume a digital-to-analog conversion system uses a 10-bit integer to represent an analog temperature over a range of -25°F to 125°F. If the actual temperature being read was 65.325°F, what would be the closest possible value that the system could represent?

(a) 59.098°F
(b) 65.294°F
(c) 65.325°F
(d) 67.552°F

Answer 1

The closest possible value that the system could represent for a temperature of 65.325°F is 65.294°F.

Step-by-step explanation:

In a digital-to-analog conversion system using a 10-bit integer, there are 2^10 (=1024) possible values that can be represented. The temperature range of -25°F to 125°F is divided into 1024 equal intervals, each representing a temperature difference of (125 - (-25)) / 1024 = 0.1471°F. To determine the closest possible value to 65.325°F, we need to find the integer value that represents the nearest temperature interval. The closest possible value in this case would be 65.325°F rounded to the nearest 0.1471°F interval, which is 65.294°F.