{The number }(1101101+1011011)₂{ can be written in decimal system as}

Correct Answer is : (200)10(200)₁0}(200)10

Correct Answer is : (200)10(200)₁0}(200)10

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UPSC NDA I and II 2020 Math Solved Paper

Question : 35 of 120

Marks: +1, -0

\text{The number }(1101101+1011011)_{2}\text{ can be written in decimal system as}

Solution:

Concept:

Convert each binary number to its decimal equivalent by summing the product of each digit and its corresponding power of 2, then add the decimals.

Explanation:

First, convert

1101101_2

to decimal.

Write it as

1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0

Compute each term:

64 + 32 + 0 + 8 + 4 + 0 + 1 = 109

1101101_2 = 109_{10}

Next, convert

1011011_2

to decimal.

Write it as

1 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0

Compute each term:

64 + 0 + 16 + 8 + 0 + 2 + 1 = 91

1011011_2 = 91_{10}

Now add the two decimals:

109 + 91 = 200

Thus

(1101101 + 1011011)_2 = (200)_{10}

Answer:

(200)_{10}

(Option C).

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