Convert `(17)_(10)` to binary system (or in base 2).

Answer

To convert the decimal number \( (17)_{10} \) to binary (base 2), we can follow these steps:

### Step 1: Identify the powers of 2
First, we need to identify the powers of 2 that are relevant for our conversion. The powers of 2 are:
- \( 2^0 = 1 \)
- \( 2^1 = 2 \)
- \( 2^2 = 4 \)
- \( 2^3 = 8 \)
- \( 2^4 = 16 \)

### Step 2: Determine which powers of 2 sum to 17
Next, we need to find which of these powers of 2 can be added together to equal 17. We can see that:
- \( 16 + 1 = 17 \)

This means we will use \( 2^4 \) (which is 16) and \( 2^0 \) (which is 1).

### Step 3: Write down the binary representation
Now, we write down the binary representation using 1s and 0s. For each power of 2:
- \( 2^4 \) (16) is included, so we write a 1.
- \( 2^3 \) (8) is not included, so we write a 0.
- \( 2^2 \) (4) is not included, so we write a 0.
- \( 2^1 \) (2) is not included, so we write a 0.
- \( 2^0 \) (1) is included, so we write a 1.

Putting this together, we have:
- \( 1 \) for \( 2^4 \)
- \( 0 \) for \( 2^3 \)
- \( 0 \) for \( 2^2 \)
- \( 0 \) for \( 2^1 \)
- \( 1 \) for \( 2^0 \)

Thus, the binary representation of \( (17)_{10} \) is \( (10001)_2 \).

### Final Answer:
The binary representation of \( (17)_{10} \) is \( (10001)_2 \).

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