If \(x\) and \(y\) are two decimal digits and \((0.1101)_2 = (0.8xy5)_{10}\),…
2021
If \(x\) and \(y\) are two decimal digits and \((0.1101)_2 = (0.8xy5)_{10}\), the decimal value of \(x+y\) is _____ .
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Correct answer: 3
Convert the binary fraction to decimal.
0.1101 (base 2) = 0.8125 (base 10).
Evaluate the binary places: 1/2 + 1/4 + 0/8 + 1/16 = 0.5 + 0.25 + 0 + 0.0625 = 0.8125.
The decimal form (0.8xy5) means 0.8 + x/100 + y/1000 + 5/10000. Set this equal to 0.8125.
Multiply both sides by 10000: 8125 = 8000 + 100x + 10y + 5. So 100x + 10y = 120, i.e. 10x + y = 12.
Digits x and y are between 0 and 9. Solve 10x + y = 12, giving x = 1 and y = 2. Thus x + y = 3.
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