Homework 2 - Data types, Operators, and Combinational logic

CE 433 Embedded Devices

2024 Spring
Name: Joel Nash
Email: jxnash@gmail.com

Tasks:

1. Work on the following problems: (20 points)
a. What are the fixed point representations of the following decimal numbers? Display your calculations and results on a paper and take a picture of it as an embedded image on your website.
20.25 in UQ16.16
128.5 in UQ16.16
0.125 in UQ.16
-38.125 in Q15.16
-50.0625 in Q15.16

b. What are the floating point representations of the following decimal numbers? Display your calculations and results on a paper and take a picture of it as an embedded image on your website.
0.141 in half precision/format
3.625 in half precision/format
-15.25 in half precision/format



Figure 1: Showing the fixed point representation asked in Task 1 (a), in this figure shows the questions worked through.
Figure 2: Showing the floating point representation asked in Task 1 (b), in this figure shows the questions worked.


Within Task 1 we work through the two methods to represent a binary number, fixed point representation and float point representation, while taking into account if it is signed/unsigned, the fractional part and the number of digits to go out to.



2. Repeat the simulation work in Section 5. Demonstrate your results in embedded videos on your website. (20 points)



                
Figure
                      3: Vivado code demonstrating the use implementing the
                      vectors and vector syntax.

                    

                


                    

                 

                  

                  Figure 4: Simulation of the code shown above, showing the
                  output of the vector.

                
            

            


                  3. Repeat all the FPGA experiments in Section 7. Demonstrate
                  your results in embedded videos on your website. (30 points)

                

            


            

            
            
 

                Figure 5:Vivado code for the home_alarm, showing the
                combinational logic.

                

                

                

                Figure 6: code showing the setup for the input switches and the
                output LEDs.

                

                

                
                

              

              

              

                Figure
                  7: Vivado code for a digital safe showing the logic
                and the in/outputs.

                

                

                
                  

                
                  Figure 8: setup code for the digital_safe with input
                switches and output LEDs.

                

                

                

                

                

                

                

              

              Figure 9: Vivado code showing the
                logic for parking_count and how that counts the spots taken.

              

              

              Figure 10: parking_count setup code
                for input switches and output LEDs.

                

                

               

            


                 4. Design a simple
                  digital system using the similar combinational logic design
                  methods shown in Section 7. Explain what the system is, show
                  the design files, demonstrate it on your FPGA. Demonstrate
                  your results in embedded videos on your website. (30 points)

            


            

            
My simple
                  digital system is an Available parking spot counter,
                using the same concept as the parking_counter in Task 3. This
                code improves on it a little by adding the feature of showing
                how many parking spots are left in the lot. In my code I set the
                maximum number of spots to 16 spots, and as the number of cars
                (switches) increases ,(goes from left to right), the LEDs
                decreasing indicate the number of spots left in binary.

            

            


              Figure 11: Vivado code for Available
                parking spots left, showing the logic and the preset (parameter)
                parking max. 

                

                

                

                Figure 12: Setup code indicating the input switches and the
                output LEDs, for available parking spots.