Let's break down the solution step by step for the Digital Logic Elevator Call System for an 8-floor building, as requested. --- ### **Step 1: Assumptions and Problem Analysis** - **Elevator has 8 floors (0 to 7).** - **There are UP and DOWN buttons on each floor (except top and bottom).** - **There are no buttons inside the elevator.** - **When a button is pressed, the elevator moves to that floor.** - **No need to track people inside.** --- ### **Step 2: Inputs and Outputs** #### **Inputs:** - **Floor Call Buttons**: Each floor has two buttons (Up, Down), except: - Floor 0: Only Up. - Floor 7: Only Down. - **Total Inputs:** \( 2 \times 8 - 2 = 14 \) (since two buttons are missing). #### **Outputs:** - **Elevator Movement Command:** Move to a specific floor (3 bits to encode 8 floors). - **Motor Direction:** Up or Down (1 bit, optional). --- ### **Step 3: State Variables** - **State:** Current position of the elevator (3 bits to represent 8 floors). - **Input:** Button pressed (encoded as a 4-bit or 3-bit value for floor number and 1 bit for direction). --- ### **Step 4: Block Diagram (Conceptual)** **Block Diagram:** ``` [Floor Call Buttons] --> [Input Encoder] --> [Elevator Controller FSM] --> [Motor Control (Move to Floor X)] ``` --- ### **Step 5: State Diagram** #### **States:** - Each state represents the elevator at a particular floor: \( S_0, S_1, ..., S_7 \). #### **Transitions:** - From any state \( S_i \), if a button for floor \( j \) is pressed (\( i \neq j \)), the next state is \( S_j \). - Output is a command to move elevator from \( S_i \) to \( S_j \). #### **Example State Diagram for 4 Floors** (for simplicity): Let’s use 4 floors (\( S_0, S_1, S_2, S_3 \)): - If at \( S_0 \) and button for floor 2 is pressed, go to \( S_2 \). - If at \( S_2 \) and button for floor 1 is pressed, go to \( S_1 \). - And so on. **Diagram (Simplified):** ``` [S0] <----> [S1] | /\ v / [S2] <--> [S3] ``` - Each arrow is labeled with the button pressed (input), and the transition is the output command to the motor. **For 8 floors, the diagram would have 8 bubbles, each with arrows going to every other bubble.** --- ### **Step 6: Flip-Flop Representation** - **3 D-type Flip-flops** to store the current floor (since \( 2^3 = 8 \)). - Next state logic (combinational) determines the next value for the flip-flops based on input (button pressed). --- ### **Step 7: K-Map and Next-State Logic** Suppose: - \( Q_2, Q_1, Q_0 \): Present state (current floor) - \( F_2, F_1, F_0 \): Floor requested (button input) **Next State:** - \( Q^+ = F \) (The elevator goes directly to requested floor; next state is input floor) **K-Map is trivial here:** - D flip-flop inputs = Button input (for direct move system) So: - \( D_2 = F_2 \) - \( D_1 = F_1 \) - \( D_0 = F_0 \) --- ### **Step 8: Output Logic** - **Motor Control:** Compare present state and requested floor to generate UP or DOWN signal. --- ### **Step 9: Final Answer Summary** #### **1. Block Diagram** ``` [Floor Call Buttons] --> [Encoder] --> [3 D Flip-Flops to store floor] --> [Compare Logic: UP/DOWN] --> [Motor] ``` #### **2. State Diagram** - 8 states (\( S_0 \) to \( S_7 \)), each state represents elevator at that floor. - Transitions from \( S_i \) to \( S_j \) on pressing button for floor \( j \). #### **3. Flip-Flop Use** - 3 D flip-flops store floor number. - D inputs are set by floor button pressed. #### **4. K-Map** - Each D input is directly the corresponding bit from the floor button pressed. --- ## **Illustrative Example (For 4 Floors):** - **States:** S0 (000), S1 (001), S2 (010), S3 (011) - **Inputs:** Button for 0,1,2,3 (encoded as 00,01,10,11) - **Next-State:** If at S0 and button for 2 (10) is pressed, next state = S2. **State Transition Table:** | Present State | Button Pressed | Next State | |:-------------:|:--------------:|:-----------:| | S0 (00) | 10 | S2 (10) | | S2 (10) | 01 | S1 (01) | | S1 (01) | 11 | S3 (11) | | ... | ... | ... | --- ## **Conclusion** - Use 3 D flip-flops to store the floor. - Next state logic: D inputs are set directly by the floor requested. - State diagram: 8 bubbles, transitions based on button pressed. - K-map: Each D input = corresponding input bit. - Output logic controls motor direction (UP/DOWN). If you need the full 8-state diagram or more detailed K-maps, let me know!