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.
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