GATE CSE 2021 Set 2 | Question: 18

Question

If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________

Comments

Another quick approach is as follows:

Just count the number of decimal places, and raise 2 to that power. Since there are four decimal places in this question, then the denominator is $2^4$. Then, just calculate the numerator as a binary number, in this case, $(1101)_2=(13)_{10}$

So the final number is $\frac{13}{2^4}=\frac{13}{16}=0.8125$.

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What if question was for base 8?

Answer 1

Answer: $3$ 

This conversion is just

$\frac{1}{2} + \frac{1}{4} + \frac{1}{16} = \frac{8 + 4 + 1}{16} = \frac{13}{16} = 0.8125$

On comparison we get $x = 1$ and $y = 2.$ Hence, $x+y= 3.$

Answer 2

Answer $= 3$

• A. $(0.1)_2 = (0.5)_{10}$
• B. $(0.01)_2 = (0.25)_{10}$
• C. $(0.001)_2 = (0.125)_{10}$
• D. $(0.0001)_2 = (0.0625)_{10}$

$A + B + D \implies (0.1101)_2 = 0.8125$

Answer 3

(0.1101)base2=(0.8xy5)base10

(1101)*2^-4=  (8xy5)*10^-4

13*25*25=8125= 8xy5

means x+y=3

 

Comments

Nice solution