To convert the binary number 101101 to its base 10 equivalent, we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand Binary Representation Binary 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 **101101**. We will 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 next digit (1) is in the \(2^3\) place. - The next digit (0) is in the \(2^4\) place. - The leftmost digit (1) is in the \(2^5\) place. So, we can represent it as follows: \[ \begin{align*} 1 & \times 2^5 \\ 0 & \times 2^4 \\ 1 & \times 2^3 \\ 1 & \times 2^2 \\ 0 & \times 2^1 \\ 1 & \times 2^0 \\ \end{align*} \] ### Step 3: Calculate Each Term Now, we will calculate the value of each term: - \(1 \times 2^5 = 1 \times 32 = 32\) - \(0 \times 2^4 = 0 \times 16 = 0\) - \(1 \times 2^3 = 1 \times 8 = 8\) - \(1 \times 2^2 = 1 \times 4 = 4\) - \(0 \times 2^1 = 0 \times 2 = 0\) - \(1 \times 2^0 = 1 \times 1 = 1\) ### Step 4: Sum All the Values Now, we will add all these values together to get the base 10 equivalent: \[ 32 + 0 + 8 + 4 + 0 + 1 = 45 \] ### Conclusion Thus, the base 10 equivalent of the binary number **101101** is **45**. ### Explanation of Other Options - **Option B (22)**: This is incorrect because the sum of the powers of 2 from the binary number does not equal 22. - **Option C (43)**: This is also incorrect for the same reason; the calculated sum does not match. - **Option D (37)**: This option is incorrect as well; the binary number does not convert to 37. ### Revision Summary - Binary numbers are converted to decimal by summing the products of each digit and its corresponding power of 2. - The binary number 101101 converts to decimal by calculating \(1 \times 32 + 0 \times 16 + 1 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1\). - The final sum of these calculations gives the base 10 equivalent, which is 45. - Always check each option against the calculated value to ensure accuracy.