The number 0.0011 in binary system represents?

Options

A. Rational number 3/8 in decimal system
B. Rational number 1/8 in decimal system
C. Rational number 3/16 in decimal system
D. Rational number 5/16 in decimal system

Answer

To convert the binary number 0.0011 to its decimal equivalent, we follow these steps:

### Step-by-Step Solution:

1. **Identify the Binary Digits**: The binary number given is 0.0011. The digits after the decimal point are 0, 0, 1, and 1.

2. **Assign Weights**: Each digit in the binary fraction has a weight based on its position. The weights for the binary fraction are calculated as follows:
- The first digit after the decimal point has a weight of \(2^{-1}\) (or \(1/2\)).
- The second digit has a weight of \(2^{-2}\) (or \(1/4\)).
- The third digit has a weight of \(2^{-3}\) (or \(1/8\)).
- The fourth digit has a weight of \(2^{-4}\) (or \(1/16\)).

3. **Multiply Each Digit by Its Weight**:
- For the first digit (0): \(0 \times 2^{-1} = 0 \times \frac{1}{2} = 0\)
- For the second digit (0): \(0 \times 2^{-2} = 0 \times \frac{1}{4} = 0\)
- For the third digit (1): \(1 \times 2^{-3} = 1 \times \frac{1}{8} = \frac{1}{8}\)
- For the fourth digit (1): \(1 \times 2^{-4} = 1 \times \frac{1}{16} = \frac{1}{16}\)

4. **Sum the Results**: Now, we sum all the results from the previous step:
\[ 0 + 0 + \frac{1}{8} + \frac{1}{16} \]

5. **Find a Common Denominator**: The common denominator for \(8\) and \(16\) is \(16\). We convert \(\frac{1}{8}\) to sixteenths:
\[ \frac{1}{8} = \frac{2}{16} \]
Now we can sum:
\[ 0 + 0 + \frac{2}{16} + \frac{1}{16} = \frac{2 + 1}{16} = \frac{3}{16} \]

6. **Final Result**: Therefore, the binary number \(0.0011\) in decimal form is \(\frac{3}{16}\).

### Summary:
The decimal equivalent of the binary number \(0.0011\) is \(\frac{3}{16}\).

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