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Decimal equivalent of (1011.011) isa.11.375b.11,370c.11.371d. 11.377

Question

Decimal equivalent of (1011.011) isa.11.375b.11,370c.11.371d. 11.377

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Solution

To convert the binary number (1011.011) to a decimal, we need to understand the place values in binary numbers.

For the whole number part (to the left of the decimal point):

  • The rightmost digit represents 2^0, the next digit to the left represents 2^1, then 2^2, and so on.

For the fractional part (to the right of the decimal point):

  • The first digit after the decimal point represents 2^-1, the next represents 2^-2, and so on.

Now, let's convert (1011.011) to decimal:

Whole number part:

  • (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11

Fractional part:

  • (0 * 2^-1) + (1 * 2^-2) + (1 * 2^-3) = 0 + 0.25 + 0.125 = 0.375

So, the decimal equivalent of (1011.011) is 11.375. Therefore, the correct answer is a. 11.375.

This problem has been solved

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