1. Experiment #3A: Introduction to Function Reduction, Function Forms, and VHDL Implementation CPE 169 Digital Design Laboratory

2. Function Reduction General approach: make function smaller Underlying purpose: make it cheaper to implement the function. True definition dependent upon how “cheaper” is defined General correlation between a “reduced function” and an inexpensive implementation

3. Minimum Cost Implementation Based on definition of “cost” Cost has no absolute definition: –Could include: Cost of components (digital IC’s, circuit board,…) Cost of development (engineering labor, tools,…) Cost of manufacturing (tooling, test fixtures,…) –Component Costs change with: current part availability and/or pricing quantity discounts changes in technology Our metrics: # of IC’s # of Gates (including NOT gates) # of Gate Inputs # of Literals Experiment 3: minimum cost defined by the number of gates required to implement function.

4. Reducing Functions Computer-based methods –fast, concise but cookbook approach Boolean algebra –instructive but slow, error prone Karnaugh Maps –fun and exciting but limited to functions of 4 - 5 variables

5. Function Forms Boolean functions can be used to describe complex operations such as adders, multipliers, etc. Infinite number of different circuits can be used to implement any given function Standard function forms: –SOP (AND/OR) –POS (OR/AND) Several common forms are derived from SOP and POS using DeMorgan’s theorem

6. DeMorgan’s Theorems Can be used to generate different function forms : SOP-based AND/OR NAND/NAND OR/NAND NOR/OR POS-based OR/AND NOR/NOR AND/NOR NAND/AND

7. Experiment 3a Procedure Overview Download circuit from CPE 169 website –.bit file (Nexys) Analyze the implemented function –Create a Truth Table (include in report!!) Reduce the function to minimized SOP & POS forms –K-Maps (include in report!!) Implement the function on the Nexys and breadboard using discrete logic IC’s: (Don’t forget detailed schematics in report!!) –NAND / NAND form (SOP) –NOR / NOR form (POS) Implement the function on the Nexys FPGA using VHDL –Using VHDL and the Xilinx Tools Compare all results –Get Instructor Sign-off Sheet & signature (include in report!)

8. Xilinx Design Methodology The steps required in order to model, simulate and implement a circuit using the Xilinx ISE software Basic steps are as simple or as complicated as you want to make them Xilinx ISE and VHDL used again in CPE 229/269/329 and CSC 315

9. Basic Xilinx Design Flow 1) VHDL source code generates a description of circuit. 2) VHDL source is translated into intermediate form for use by other software used in the design flow. 3) Test Bench Waveform software generates signals to verify circuit operation using the ModelSim XE simulator. 4) Circuit inputs and outputs are “mapped” to FPGA pins externally hardwired to I/O devices on the Nexys board. 5) The circuit design is downloaded into the FPGA. (Use Digilent ExPORT for Nexys USB port) 6) Proper operation of the circuit is verified.

11. Create a New VHDL Source Module & Define Inputs/Outputs

12. Add your logic expression to the VHDL code module template Your definition of input / output signals is turned into a VHDL “Entity” Insert code here

14. Circuit Connections to Development Board Nexys-2 Board SW1 SW2 SW3 SW4 FPGA H18 K18 K17 L14 J14 J15 K15 K14 LDO LD1 LD2 LD3 Assign Package Pins -Maps Input/Output Circuit Signals to FPGA Pins -Puts Info in a “Constraints” File ABCDABCD F1 F2

18. A Little “Sage Advice” Since this is your first time using the tools, be sure to follow all of the steps, in the order given.Since this is your first time using the tools, be sure to follow all of the steps, in the order given. –Skipping steps may result in horrendously hideous outcomes that you really don’t want to experience. –A confused CAD tool is not a happy CAD tool! ;( Be sure to read the Explanations as you proceed, so that you begin to understand why you are doing what you are doingBe sure to read the Explanations as you proceed, so that you begin to understand why you are doing what you are doing.

19. Note for Next Week Be sure to run through the B2 Spice A/D Tutorial (on the CPE-169 website) Brief overview of the logic circuit simulation tool you will be using in next week’s lab BEFORE LAB: