To convert the binary number (11001_2) to its decimal (base ten) equivalent, we will follow a systematic approach. Let's break it down step-by-step. Step 1: Understand the Binary System The binary system is a base-2 numeral system that uses only two digits: 0 and 1. Each digit in a binary number represents a power of 2, starting from the rightmost digit, which represents (2^0). Step 2: Write Down the Binary Number The binary number we have is (11001_2). We can label each digit with its corresponding power of 2:

• The rightmost digit (1) is in the (2^0) place.
• The next digit to the left (0) is in the (2^1) place.
• The next digit (0) is in the (2^2) place.
• The next digit (1) is in the (2^3) place.
• The leftmost digit (1) is in the (2^4) place.

So, we can represent (11001_2) as follows: [ 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 ] Step 3: Calculate Each Term Now, we will calculate the value of each term:

• (1 \cdot 2^4 = 1 \cdot 16 = 16)
• (1 \cdot 2^3 = 1 \cdot 8 = 8)
• (0 \cdot 2^2 = 0 \cdot 4 = 0)
• (0 \cdot 2^1 = 0 \cdot 2 = 0)
• (1 \cdot 2^0 = 1 \cdot 1 = 1)

Step 4: Sum the Values Now, we add all these values together: [ 16 + 8 + 0 + 0 + 1 = 25 ] Conclusion Thus, the decimal (base ten) equivalent of the binary number (11001_2) is 25. Explanation of Options

• A. 20: This is incorrect because the sum of the powers of 2 calculated does not equal 20.
• B. 25: This is the correct answer, as shown in the calculations above.
• C. 28: This is incorrect; it does not match the calculated sum of the binary conversion.
• D. 30: This is also incorrect; the sum of the binary conversion does not reach 30.

Revision Summary

• The binary number (11001_2) can be converted to decimal by summing the products of each binary digit and its corresponding power of 2.
• The calculation yields (16 + 8 + 0 + 0 + 1 = 25).
• The correct answer is B. 25.
• Understanding the binary to decimal conversion process is crucial for working with different numeral systems in computer science.