13 votes 13 votes If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________ Digital Logic gatecse-2021-set2 numerical-answers digital-logic number-representation 1-mark + – Arjun asked Feb 18, 2021 retagged Nov 30, 2022 by Lakshman Bhaiya Arjun 4.8k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply jatinmittal199510 commented Apr 11, 2021 reply Follow Share 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 $\frac{13}{2^4}=\frac{13}{16}=0.8125$. 7 votes 7 votes Answers Copied commented Jan 11 reply Follow Share What if question was for base 8? 0 votes 0 votes Please log in or register to add a comment.
Best answer 12 votes 12 votes 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, $x+y= 3.$ witness_07 answered Feb 18, 2021 selected Apr 4, 2021 by Arjun witness_07 comment Share Follow See all 0 reply Please log in or register to add a comment.
13 votes 13 votes Answer $= 3$ $(0.1)_2 = (0.5)_{10}$ $(0.01)_2 = (0.25)_{10}$ $(0.001)_2 = (0.125)_{10}$ $(0.0001)_2 = (0.0625)_{10}$ $A + B + D \implies (0.1101)_2 = 0.8125$ jatinmittal199510 answered Feb 18, 2021 edited Apr 4, 2021 by Arjun jatinmittal199510 comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes (0.1101)base2=(0.8xy5)base10 (1101)*2^-4= (8xy5)*10^-4 13*25*25=8125= 8xy5 means x+y=3 Chandrabhan Vishwa 1 answered Dec 9, 2021 edited Oct 28, 2022 by Chandrabhan Vishwa 1 Chandrabhan Vishwa 1 comment Share Follow See 1 comment See all 1 1 comment reply Riyaz Ahmad commented Jul 5, 2023 reply Follow Share Nice solution 1 votes 1 votes Please log in or register to add a comment.