To find the decimal equivalent of the binary number 101101, we will break down the process 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 **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 (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 the binary number as follows: \[ 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 \] ### Step 3: Calculate Each Term Now, we will calculate the value of each term: - \(1 \cdot 2^5 = 1 \cdot 32 = 32\) - \(0 \cdot 2^4 = 0 \cdot 16 = 0\) - \(1 \cdot 2^3 = 1 \cdot 8 = 8\) - \(1 \cdot 2^2 = 1 \cdot 4 = 4\) - \(0 \cdot 2^1 = 0 \cdot 2 = 0\) - \(1 \cdot 2^0 = 1 \cdot 1 = 1\) ### Step 4: Add the Values Together Now, we will add all these values together: \[ 32 + 0 + 8 + 4 + 0 + 1 = 45 \] ### Conclusion The decimal equivalent of the binary number **101101** is **45**. ### Explanation of Other Options Now, let's analyze the other options to understand why they are incorrect: - **Option B: 22** - If we were to convert 22 back to binary, it would be 10110, which does not match our original binary number of 101101. - **Option C: 27** - The binary representation of 27 is 11011, which again does not match 101101. - **Option D: 53** - The binary representation of 53 is 110101, which is also different from 101101. ### Revision Summary - Binary numbers are base-2 and each digit represents a power of 2. - To convert binary to decimal, multiply each digit by its corresponding power of 2 and sum the results. - The binary number 101101 converts to decimal as follows: \(1 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 1 \cdot 4 + 0 \cdot 2 + 1 \cdot 1 = 45\). - The correct answer is **A. 45**; other options do not match the binary number provided.