You're right; the **Red-Red** state is essential in traffic light systems to ensure a brief interval when both directions display red, preventing any cross-traffic conflicts. This state typically appears between transitions from one direction's green/yellow sequence to the other’s green light.

### Revised Design for Questions 3 and 4

### Question 3 - Standby Mode with Red-Red State

#### **Design Process with Red-Red State:**

1. **Traffic Light Sets and Mode Definition (including Red-Red):**
   - We will add the Red-Red state between each set’s green/yellow sequence, totaling five states in the sequence:
     - **State 1**: Set 1 (Green), Set 2 (Red)
     - **State 2**: Set 1 (Yellow), Set 2 (Red)
     - **State 3**: Set 1 (Red), Set 2 (Red)  ⟶ Red-Red state
     - **State 4**: Set 1 (Red), Set 2 (Green)
     - **State 5**: Set 1 (Red), Set 2 (Yellow)
     - After State 5, return to State 3 (Red-Red) and continue the cycle.

2. **Timing and State Representation:**
   - Each state should still have a 3-second interval.
   - Assign binary values to represent each state:
     - **State 1 (Green-Red)**: 000
     - **State 2 (Yellow-Red)**: 001
     - **State 3 (Red-Red)**: 010
     - **State 4 (Red-Green)**: 011
     - **State 5 (Red-Yellow)**: 100

3. **K-Map Minimization:**
   - Create K-maps to determine minimized Boolean expressions for each light output (G1, Y1, R1, G2, Y2, R2), considering the additional Red-Red state.

### Question 4 - Walk Mode with Red-Red State

#### **Design Process for Walk Mode with Red-Red State:**

1. **Trigger Walk Mode via Pedestrian Button:**
   - When the pedestrian button is pressed during the Red-Red state (State 3), keep both R1 and R2 active for an extra 3 seconds, then return to Standby Mode.
   - If the button is pressed in other states, Walk Mode will activate only once the system returns to the next Red-Red state.

2. **Latch Design for Button Press in Walk Mode:**
   - Use a latch to store the Walk Mode activation signal when the button is pressed.
   - The latch resets after the extended Red-Red state, preventing multiple activations of Walk Mode within one cycle.

3. **K-Map Minimization with Walk Mode:**
   - Use the Walk Mode latch signal in the K-map to define the conditions under which Red-Red holds for the extra interval.
   - Derive minimized expressions for R1 and R2 to remain red during this extended period.

### Verification Steps for Both Questions

1. **Simulate All States:**
   - Verify that the Red-Red state functions correctly between transitions.
   - Confirm the entire sequence operates correctly: Green-Red → Yellow-Red → Red-Red → Red-Green → Red-Yellow → Red-Red, repeating as needed.

2. **Test Walk Mode:**
   - Press the pedestrian button during various states and ensure Walk Mode only activates during the Red-Red state.
   - Confirm that both R1 and R2 stay red for an additional 3 seconds when Walk Mode is active.
  
This complete design now includes the Red-Red state for both questions and will ensure smooth operation and safety in traffic control. Let me know if there’s anything more specific you’d like me to elaborate on!

solve the design equations of 3 and 4 using k map and verify the answers or solution two times before answering it