To convert the binary number (11001_2) to its decimal (base 10) equivalent, we will follow a systematic approach. Let's break it down step-by-step. Step-by-Step Conversion

1. Understanding Binary Representation:
2. Binary is a base-2 numeral system that uses only two digits: 0 and 1.
3. Each digit in a binary number represents a power of 2, starting from the rightmost digit, which represents (2^0).
4. Identifying the Positions:
5. The binary number (11001_2) has five digits. We will label the positions from right to left:
   • Position 0: (1) (which is (2^0))
   • Position 1: (0) (which is (2^1))
   • Position 2: (0) (which is (2^2))
   • Position 3: (1) (which is (2^3))
   • Position 4: (1) (which is (2^4))
6. Calculating the Decimal Value:
7. Now, we will calculate the decimal value by multiplying each binary digit by its corresponding power of 2 and then summing the results: [ \text{Decimal Value} = (1 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) ]
8. Breaking it down:
   • (1 \times 2^4 = 1 \times 16 = 16)
   • (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)
9. Summing the Values:
10. Now, we add these results together: [ 16 + 8 + 0 + 0 + 1 = 25 ]

Conclusion The decimal equivalent of the binary number (11001_2) is 25. Therefore, the correct answer is C. Explanation of Other Options

• Option A: 30 - This is incorrect because the sum of the powers of 2 calculated does not reach 30. The maximum value from the binary digits provided is 25.
• Option B: 28 - This is also incorrect for the same reason as option A. The calculations do not support this value.
• Option D: 20 - This is incorrect as well. The binary number (11001_2) clearly sums to 25, not 20.

Revision Summary

• Binary numbers are converted to decimal by summing the products of each digit and its corresponding power of 2.
• The binary number (11001_2) translates to (1 \times 16 + 1 \times 8 + 0 \times 4 + 0 \times 2 + 1 \times 1).
• The final sum of these products gives the decimal value of 25.
• The correct answer is C: 25.