The resolution of an 8bit unsigned binary fixedpoint number

The resolution of an 8-bit unsigned binary fixed-point number is 2-2, which equals 1/4. What is the value of the number if the integer stored in memory is 81?

Solution

81₁₀ = 01010001₂

The actual number is then 010100.01₂

Converting the whole number part 010100 = 1*2² + 1*2⁴ = 20

Converting the fraction part .01 = 0*2^-1 + 1*2^-2 = 0.25

So the complete number is 20.25