A number in binary system is 110001. It is equal to which one of the following numbers in decimal system?

Options

A. 45
B. 46
C. 48
D. 49

Answer

To convert the binary number 110001 to its decimal equivalent, we follow these steps:

### Step-by-Step Solution:

1. **Identify the Binary Number**: The given binary number is 110001.

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 is \(2^0\), the next one to the left is \(2^1\), and so on.
- The binary number can be broken down as follows:
- \(1 \times 2^5\) (for the leftmost 1)
- \(1 \times 2^4\)
- \(0 \times 2^3\)
- \(0 \times 2^2\)
- \(0 \times 2^1\)
- \(1 \times 2^0\) (for the rightmost 1)

3. **Calculate Each Term**:
- \(1 \times 2^5 = 1 \times 32 = 32\)
- \(1 \times 2^4 = 1 \times 16 = 16\)
- \(0 \times 2^3 = 0 \times 8 = 0\)
- \(0 \times 2^2 = 0 \times 4 = 0\)
- \(0 \times 2^1 = 0 \times 2 = 0\)
- \(1 \times 2^0 = 1 \times 1 = 1\)

4. **Sum All the Values**:
- Now, add all the calculated values together:
\[ 32 + 16 + 0 + 0 + 0 + 1 = 49 \]

5. **Conclusion**: The decimal equivalent of the binary number 110001 is **49**.