1. The problem is to convert the binary number $101101_2$ to its decimal (base 10) equivalent. 2. Each digit in a binary number represents a power of 2, starting from the rightmost digit which is $2^0$. 3. Write down the place values for each digit in $101101_2$ from right to left: $$2^5, 2^4, 2^3, 2^2, 2^1, 2^0$$ 4. Multiply each binary digit by its corresponding power of 2: $$1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0$$ 5. Calculate each term: $$1 \times 32 + 0 \times 16 + 1 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1 = 32 + 0 + 8 + 4 + 0 + 1$$ 6. Add the results: $$32 + 8 + 4 + 1 = 45$$ 7. Therefore, the decimal equivalent of $101101_2$ is $45$.