Topic: Digital Logic
If x and y are two decimal numbers such as $(0.11101)_{2}=(0.90xy5)_{10}$, what are the values of x and y?
- A. x=2, y=6
- B. x=6, y=2
- C. x=9, y=8
- D. none of the above
Answer: B. x=6, y=2
Explanation: Convert the binary fraction $(0.11101)_2$ to decimal:
$(0.11101)_2 = 1\times2^{-1} + 1\times2^{-2} + 1\times2^{-3} + 0\times2^{-4} + 1\times2^{-5}$
$= 0.5 + 0.25 + 0.125 + 0 + 0.03125 = 0.90625_{10}$.
Comparing $0.90625$ with $0.90xy5$, we get $x=6$ and $y=2$.