What is (1000000001)₂ - (0.0101)₂ equal to?

Correct Answer is : (512.6875)10(512.6875)₁0}(512.6875)10

Correct Answer is : (512.6875)10(512.6875)₁0}(512.6875)10

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UPSC NDA II 2015 Mathematics Paper

Question : 1 of 120

Marks: +1, -0

What is

(1000000001)_{2} - (0.0101)_{2}

equal to?

Solution:

Concept:

Convert binary numbers to decimal by summing each digit multiplied by its positional power of 2.

Explanation:

Convert

(1000000001)_2

to decimal:

1 \times 2^9 + 1 \times 2^0 = 512 + 1 = 513

Convert

(0.0101)_2

to decimal:

1 \times 2^{-2} + 1 \times 2^{-4} = \frac{1}{4} + \frac{1}{16} = \frac{5}{16} = 0.3125

Subtract:

513 - 0.3125 = 512.6875

Thus the result in base‑10 is

(512.6875)_{10}

Answer:

(512.6875)_{10}

(Option B).

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