1. Problem: Design circuits for the output equation $Vo = 2V1 + 4V2 + 3V3$. 2. Identify constants and variables: The output voltage $Vo$ depends on inputs $V1$, $V2$, and $V3$ with constants 2, 4, and 3 respectively. 3. Mathematical expression: $$Vo = 2V1 + 4V2 + 3V3$$ 4. Explanation: To design this circuit, recall that multiplying an input voltage by a constant corresponds to an amplifier gain. 5. Step 1: Amplify $V1$ by 2 to get $2V1$. 6. Step 2: Amplify $V2$ by 4 to get $4V2$. 7. Step 3: Amplify $V3$ by 3 to get $3V3$. 8. Step 4: Sum all amplified signals: $2V1 + 4V2 + 3V3$ to obtain $Vo$. 9. Circuit implication: Use amplifiers with gains 2, 4, and 3 for each input followed by a summing amplifier to add the signals. --- 1. Problem: Design circuits for the output equation $Vo = 2V1 - 3V2 + 3V3 - V4$. 2. Identify constants and variables: The output voltage $Vo$ depends on inputs $V1$, $V2$, $V3$, and $V4$ with constants 2, -3, 3, and -1 respectively. 3. Mathematical expression: $$Vo = 2V1 - 3V2 + 3V3 - V4$$ 4. Explanation: Similar to the previous example, coefficients indicate amplifier gains; negative signs represent inversion. 5. Step 1: Amplify $V1$ by 2 to get $2V1$. 6. Step 2: Amplify $V2$ by 3 and invert to get $-3V2$. 7. Step 3: Amplify $V3$ by 3 to get $3V3$. 8. Step 4: Amplify $V4$ by 1 and invert to get $-V4$. 9. Step 5: Sum all signals: $2V1 + (-3V2) + 3V3 + (-V4) = 2V1 - 3V2 + 3V3 - V4$. 10. Circuit implication: Use amplifiers with appropriate gains and polarity, then a summing amplifier. Final answers: The circuit designs involve scaling inputs by specified constants and summing them according to the equation signs.