Experiment 2 Questions 1. There are two methods that can be used on generate a complement function using a 2-input NAND gate. Draw a diagram detailing these two methods and explain how they work. Consider using the associated truth table in your explanation. 2. Answer the previous question for the 4-input NAND gate (7420). 3. An XOR gate can also be used as an inverter. Draw a circuit diagram detailing how this is done. Use a truth table in your description.

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

Minimum Cost Implementation Based on definition of “cost” Cost has not absolute definition: based on: –current part availability and/or pricing –quantity discounts –changes in technology Experiment 3: minimum cost defined by the number of gates required to implement function.

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 four variables

Function Forms Boolean function used to describe use 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

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

Experiment 3 Procedure Overview Download circuit from CPE 169 website (JEDEC file) Analyze the implemented function Implement the function on the XCRP board using discrete logic: –NAND/NAND form –NOR/NOR form Compare results