Consider sampling quantizing digitizing analog temperatures

Consider sampling (quantizing, digitizing) analog temperatures in the range from -144 to 41 °F. If you use 16 bits per sample, what does the binary value 1111 represent?

Solution

As you specified, we are using 16 bits per sample.

And we are trying to represent a total of 186 values from -144 to 41.

As you have to represent a signed magnitude, i.e., both positive and negative number, the Most Significand Bit is reserved to sign, and the remaining 15 bits are used to represent the actual value.

The binary value 1111 is stored in the 16-bit format as:

0000 0000 0000 1111. Therefore, converting this to decimal value: As the MSB is 0, which means its a positive number. And 1111₂ = 15₁₀. Therefore, the given binary value is equivalent to 15^oF.