1. **State the problem:** Add the binary numbers $101.011$ and $11.1101$. 2. **Understand binary addition:** Binary addition works like decimal addition but only with digits 0 and 1. The rules are: - $0 + 0 = 0$ - $0 + 1 = 1$ - $1 + 0 = 1$ - $1 + 1 = 10$ (which means write 0 and carry 1 to the next higher bit) 3. **Align the numbers by the binary point:** $$ \begin{array}{r} 101.0110 \\ +\ 11.1101 \end{array} $$ Note: Added a trailing zero to $101.011$ to match the number of fractional digits. 4. **Add from right to left:** - Fractional part: - $0 + 1 = 1$ - $1 + 0 = 1$ - $1 + 1 = 10$ (write 0, carry 1) - $0 + 1 + 1 (carry) = 10$ (write 0, carry 1) - Integer part: - $1 + 1 + 1 (carry) = 11$ (write 1, carry 1) - $0 + 1 + 1 (carry) = 10$ (write 0, carry 1) - $1 + 0 + 1 (carry) = 10$ (write 0, carry 1) - Carry 1 remains, write it as the new leftmost bit. 5. **Write the result:** $$1101.0011$$ 6. **Explanation:** The sum of $101.011_2$ and $11.1101_2$ is $1101.0011_2$. 7. **Optional verification in decimal:** - $101.011_2 = 5 + 0.25 + 0.125 = 5.375$ - $11.1101_2 = 3 + 0.5 + 0.25 + 0.0625 = 3.8125$ - Sum $= 5.375 + 3.8125 = 9.1875$ - $1101.0011_2 = 8 + 4 + 0 + 1 + 0.0 + 0.0 + 0.125 + 0.0625 = 9.1875$ This confirms the binary addition is correct.