Experiments

 

 

 

Experiment No. 2: Simplification of Boolean Functions

 

Objectives
  • Although a Boolean function is uniquely defined by its truth table, when expressed algebraically, the function may appear in many different forms. Since the cost of implementing a Boolean function is directly related to the Boolean expression from which the function is implemented, simplifying a function can reduce the cost of implementation.
  • The Karnaugh Map (K-map) is a tool for simplifying Boolean functions. The simplified expressions resulting from this method are in either SOP (sum-of-products) form for NAND-NAND implementation, or POS (product-of-sums) form for NOR-NOR implementation. This experiment uses K-Maps to simplify Boolean functions and to implement them by using NAND gates and NOR gates.

Procedure
  1. Create a folder (directory) called F1_SOP. The following project will be placed within this folder. Using the MAX+plusII software, use the schematic technique to construct the following circuit:


Simplify the Boolean function F1(w, x, y, z) = S(1, 2, 4, 6, 9, 10, 12, 14) and design a circuit with 2-input NAND gates only to realize the function. 

Please have hand-drawn truth tables/waveforms and schematics for each of the functions below completed before you start the lab. For this experiment, you should also include the K-maps that you have used to simplify the function.
 

  1. Simplify the same Boolean function F1 to the POS form and design a circuit with 2-input NOR gates only to realize the function. Use the schematic technique and save this project in the folder (directory) F1_POS.

 

  1. Assume that F1 also contains "don't care" points S(5, 8, 13). Simplify the function to SOP form and POS form, and implement the function by using 2-input NAND gates and NOR gates, respectively. Use the schematic technique and save the project with the SOP function in a folder (directory) called SOP_DC and the project with the POS function in the folder called POS_DC.


Are these two circuits equivalent to each other? Justify your answer.   (Note: Two circuits are said to be equivalent if they implement the same truth table.)

What to turn in
  • F1_SOP - contains 1 project (F1_SOP)
  • F1_POS - contains 1 project (F1_POS)
  • POS_DC - contains 1 project (POS_DC)
  • SOP_DC - contains 1 project (SOP_DC)