To convert the binary number 1101 to its base 10 equivalent, we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understanding Binary Numbers Binary numbers are base 2 numbers, which means they only use 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 1101. 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 (1) is in the \(2^2\) place. - The leftmost digit (1) is in the \(2^3\) place. So, we can represent the binary number 1101 as follows: \[ \begin{align*} 1 & \times 2^3 \\ 1 & \times 2^2 \\ 0 & \times 2^1 \\ 1 & \times 2^0 \\ \end{align*} \] ### Step 3: Calculate Each Term Now, we will calculate the value of each term: - \(1 \times 2^3 = 1 \times 8 = 8\) - \(1 \times 2^2 = 1 \times 4 = 4\) - \(0 \times 2^1 = 0 \times 2 = 0\) - \(1 \times 2^0 = 1 \times 1 = 1\) ### Step 4: Add the Values Together Next, we add all these values together to get the base 10 equivalent: \[ 8 + 4 + 0 + 1 = 13 \] ### Conclusion Thus, the base 10 equivalent of the binary number 1101 is **13**. Therefore, the correct option is **B**. ### Explanation of Other Options - **A. 11**: This is incorrect because the sum of the calculated values (8 + 4 + 0 + 1) does not equal 11. - **C. 14**: This is also incorrect. The calculated sum is less than 14, so it cannot be the correct answer. - **D. 15**: This option is incorrect as well. The sum of the values is not high enough to reach 15. ### Common Pitfalls - **Miscounting Powers**: Ensure you start counting powers from \(2^0\) on the right. - **Forgetting to Add All Terms**: Always remember to add all the calculated values together. - **Confusing Binary with Decimal**: Remember that binary is base 2, while decimal is base 10. ### Revision Summary - Binary numbers use powers of 2 for each digit. - Convert each binary digit to its decimal equivalent by multiplying by the corresponding power of 2. - Add all the decimal values together to find the base 10 equivalent. - The binary number 1101 equals 13 in decimal (base 10).