To find the decimal equivalent of the binary number 101101, we will follow a step-by-step process to convert it from binary (base 2) to decimal (base 10). ### Step-by-Step Explanation 1. **Understanding Binary Numbers**: - Binary numbers are composed of only two digits: 0 and 1. Each digit represents a power of 2, starting from the rightmost digit, which represents \(2^0\). 2. **Identifying the Place Values**: - For the binary number 101101, we can break it down as follows: - 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 leftmost digit (1) is in the \(2^4\) place. So, we can write the binary number with its corresponding powers of 2: \[ 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 \] 3. **Calculating Each Term**: - Now, we calculate each term: - \(1 \cdot 2^5 = 1 \cdot 32 = 32\) - \(0 \cdot 2^4 = 0 \cdot 16 = 0\) - \(1 \cdot 2^3 = 1 \cdot 8 = 8\) - \(1 \cdot 2^2 = 1 \cdot 4 = 4\) - \(0 \cdot 2^1 = 0 \cdot 2 = 0\) - \(1 \cdot 2^0 = 1 \cdot 1 = 1\) 4. **Adding the Values Together**: - Now, we add all these values together: \[ 32 + 0 + 8 + 4 + 0 + 1 = 45 \] ### Conclusion The decimal equivalent of the binary number 101101 is **45**. Therefore, the correct option is **A**. ### Explanation of Other Options - **B. 22**: This value does not correspond to any combination of the powers of 2 represented in the binary number 101101. - **C. 23**: This is also incorrect as it does not match the calculated total of 45. - **D. 30**: This option is incorrect for the same reason; it does not match the calculated total. ### Revision Summary - Binary numbers are converted to decimal by summing the products of each binary digit and its corresponding power of 2. - The binary number 101101 translates to \(1 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 1 \cdot 4 + 0 \cdot 2 + 1 \cdot 1\). - The final sum of these products gives the decimal equivalent, which is 45. - The correct answer is option A (45).