GATE CS Mastery
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GATE CS 2021 Set 2 · Digital Logic

Question 28

NATPrinted as CS Q.181 markNo negative markingEasy (estimate)

Question

If xx and yy are two decimal digits and (0.1101)2=(0.8xy5)10(0.1101)_2 = (0.8xy5)_{10}, the decimal value of x+yx + y is ______.

Official answer and solution
Official answer
3
From
Official GATE 2021 answer key

Solution

Convert the fractional binary number to its decimal representation and match digit by digit.

Convert (0.1101)2(0.1101)_2 to decimal:

(0.1101)2=1⋅2−1+1⋅2−2+0⋅2−3+1⋅2−4(0.1101)_2 = 1 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3} + 1 \cdot 2^{-4}
(0.1101)2=0.5+0.25+0+0.0625=0.812510(0.1101)_2 = 0.5 + 0.25 + 0 + 0.0625 = 0.8125_{10}

Comparing 0.81250.8125 with the given decimal format 0.8xy50.8xy5:

  • The first decimal place is 88.
  • The second decimal place is x=1x = 1.
  • The third decimal place is y=2y = 2.
  • The fourth decimal place is 55.

Thus, x=1x = 1 and y=2y = 2. The sum is:

x+y=1+2=3x + y = 1 + 2 = 3
Final answer

3

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2021 Computer Science and Information Technology - Session 2 (CS2)
Question
28 of 65, printed as CS Q.18
Section
Computer Science and Information Technology

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