1. **State the problem:** We have a logic circuit with inputs A and B. An OR gate takes A and B as inputs and outputs C. B is also routed directly to D. An AND gate takes C and D as inputs and outputs Q. We need to complete the truth table for inputs A, B, C, D, and output Q. 2. **Recall logic gate formulas:** - OR gate: $$C = A + B$$ (output is 1 if A or B is 1) - AND gate: $$Q = C \cdot D$$ (output is 1 only if both C and D are 1) 3. **Calculate intermediate values for each input combination:** | A | B | C = A + B | D = B | Q = C \cdot D | |---|---|-----------|-------|--------------| | 0 | 0 | 0 + 0 = 0 | 0 | 0 \cdot 0 = 0 | | 0 | 1 | 0 + 1 = 1 | 1 | 1 \cdot 1 = 1 | | 1 | 0 | 1 + 0 = 1 | 0 | 1 \cdot 0 = 0 | | 1 | 1 | 1 + 1 = 1 | 1 | 1 \cdot 1 = 1 | 4. **Complete the truth table:** | A | B | C | D | Q | |---|---|---|---|---| | 0 | 0 | 0 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 1 | **Final answer:** $$\begin{array}{ccccc} A & B & C & D & Q \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 \end{array}$$