What is `(1001)_(2)` equal to?

Options

A. `(5)_(10)`
B. `(9)_(10)`
C. `(17)_(10)`
D. `(11)_(10)`

Answer

To convert the binary number \( (1001)_2 \) to its decimal equivalent, we will follow these steps:

### Step 1: Write down the binary number and its positional values
The binary number \( 1001_2 \) can be broken down into its positional values. Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is \( 2^0 \)).

- The binary number is \( 1 \, 0 \, 0 \, 1 \).
- The positional values are:
- \( 1 \) at \( 2^3 \)
- \( 0 \) at \( 2^2 \)
- \( 0 \) at \( 2^1 \)
- \( 1 \) at \( 2^0 \)

### Step 2: Calculate the decimal value
Now, we will calculate the decimal value by multiplying each binary digit by its corresponding power of 2:

\[ 1 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 \]

Calculating each term:
- \( 1 \times 2^3 = 1 \times 8 = 8 \)
- \( 0 \times 2^2 = 0 \times 4 = 0 \)
- \( 0 \times 2^1 = 0 \times 2 = 0 \)
- \( 1 \times 2^0 = 1 \times 1 = 1 \)

### Step 3: Add the results
Now, we will add all the results together:

\[ 8 + 0 + 0 + 1 = 9 \]

### Conclusion
Thus, the decimal equivalent of the binary number \( (1001)_2 \) is \( 9 \).

### Final Answer
\[ (1001)_2 = 9_{10} \]

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