1. **Problem:** Simplify $101_2 + 111_2$. 2. **Formula and Rules:** To add binary numbers, align them by their least significant bit and add digit by digit, carrying over when the sum exceeds 1. 3. **Step-by-step Addition:** Write the numbers: $$101_2$$ $$+111_2$$ Add from right to left: - $1 + 1 = 10_2$ (write 0, carry 1) - $0 + 1 + 1 (carry) = 10_2$ (write 0, carry 1) - $1 + 1 + 1 (carry) = 11_2$ (write 1, carry 1) Since there is a carry left, write it down: Final sum: $$1100_2$$ 4. **Explanation:** Adding binary numbers is similar to decimal addition but carries occur when sum is 2 or more. 5. **Answer:** The sum of $101_2$ and $111_2$ is $1100_2$. **Final answer:** $1100_2$