The binary number 10110100001 in decimal system is:

Options

A. 441
B. 1441
C. 1241
D. 241

Answer

To convert the binary number 10110100001 to decimal, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the binary number**: The binary number given is 10110100001.

2. **Assign powers of 2**: Starting from the rightmost digit (which is the least significant bit), assign powers of 2 to each digit. The rightmost digit corresponds to \(2^0\), the next one to \(2^1\), and so on up to \(2^{10}\) for the leftmost digit.

- The powers of 2 for each position are:
- \(2^{10}\) for the leftmost 1
- \(2^9\) for the next 0
- \(2^8\) for the next 1
- \(2^7\) for the next 1
- \(2^6\) for the next 0
- \(2^5\) for the next 1
- \(2^4\) for the next 0
- \(2^3\) for the next 0
- \(2^2\) for the next 0
- \(2^1\) for the next 0
- \(2^0\) for the rightmost 1

3. **Write down the contributions**: Now, we will multiply each binary digit by its corresponding power of 2:
- \(1 \times 2^{10} = 1 \times 1024 = 1024\)
- \(0 \times 2^{9} = 0 \times 512 = 0\)
- \(1 \times 2^{8} = 1 \times 256 = 256\)
- \(1 \times 2^{7} = 1 \times 128 = 128\)
- \(0 \times 2^{6} = 0 \times 64 = 0\)
- \(1 \times 2^{5} = 1 \times 32 = 32\)
- \(0 \times 2^{4} = 0 \times 16 = 0\)
- \(0 \times 2^{3} = 0 \times 8 = 0\)
- \(0 \times 2^{2} = 0 \times 4 = 0\)
- \(0 \times 2^{1} = 0 \times 2 = 0\)
- \(1 \times 2^{0} = 1 \times 1 = 1\)

4. **Sum the contributions**: Now, we will add all the contributions together:
- \(1024 + 0 + 256 + 128 + 0 + 32 + 0 + 0 + 0 + 0 + 1 = 1024 + 256 + 128 + 32 + 1\)

5. **Calculate the total**:
- First, add \(1024 + 256 = 1280\)
- Then, add \(1280 + 128 = 1408\)
- Next, add \(1408 + 32 = 1440\)
- Finally, add \(1440 + 1 = 1441\)

6. **Final Result**: The decimal equivalent of the binary number 10110100001 is **1441**.