Site last updated
9/12/03

MINIMIZING DIGITAL LOGIC USING K-MAPS, CODE CONVERSION, AND CONTINUING LOGIC DESIGN/SIMULATION

Objectives:
1.  To use the knowledge learned in Lab 1 to design more complicated circuits.
2.  To become familiar with code converters and incorporating LEDs into design testing.
3.  To use ISE 4.2i to create a circuit and simulate it. 
4.  Explore different K-Map reduction software.

There are five parts to this lab.

Part 1:  Given the following Boolean function in three variables:
              F1(X,Y,Z) = X'Z' + X'YZ + XY'Z'
(A)  Fill out the truth table for F1 in the work sheet.
(B)  Immediately below the truth table for F1 is a K-map. Fill out the K-map.
(C)  Use the K-map to simplify the Boolean function. Call it F2. Show your work.
(D)  Design F1 using AND and OR gates and F2 using only NAND gates and inverters. There are three inputs: X, Y, and Z and their complements.  There are two outputs: F1 (original) and F2 (simplified)  Use the gates as stated above.  Draw layout diagrams giving the relative position of the chips on the breadboard.  Draw logic diagrams.
(E)  Implement both circuits. Connect the same inputs to both circuits and record the outputs for both. Verify that circuit operation agrees with the truth table.

Internet students use Winbreadboard to construct and simulate the circuit.  Regular students build the circuit on the logic trainer in the lab and demonstrate the circuit to the lab teaching assistant (TA).

Part 2: A function with four variables

Here is a Boolean function of four variables:
             F3=A'B'D + BC'D + A'BC + ACD
(A)  Fill out the truth table for F3 in the work sheet.
(B)  Immediately below the truth table for F3 is a K-map. Fill out the K-map.
(C)  Use it to simplify the Boolean function. Show your work.
(D)  Design the simplified circuit using any 7400 logic you wish.   There are four inputs: A, B, C, and D (along with the complements).  There is one output: F3.  Draw a layout diagram giving the relative position of the chips on the breadboard.  Draw a logic diagram.

Internet students use Winbreadboard to construct and simulate the circuit.  Regular students build the circuit on the logic trainer in the lab and demonstrate the circuit to the lab teaching assistant (TA).  Verify that the circuit operation agrees with the truth table.

Part 3:  Code Conversion:  8421 Code to 84-2-1 Code.

The table below gives the relationship between 8421 and 84-2-1 codes.  The left-hand side of the table is the input and the right-hand side is the output.

A.  Design the circuit on paper.
  1).  Design the code converter using whatever components you like (NAND, NOR, AND-OR, MUX) with the goal of minimizing the circuitry.
  2).   It will have four inputs: A, B, C, and D (ordered from left to right on the switches).
  3).  It will have four outputs:  W, X, Y, and Z (ordered left to right or top to bottom on the LEDs).
  4).  Draw a layout diagram giving the relative position of the chips on the breadboard.
  5).  Draw a logic diagram.

B.  Internet students use Winbreadboard to construct and simulate the circuit.  Regular students build the circuit on the logic trainer and demonstrate the circuit to the lab teaching assistant (TA).  Verify that the circuit operation agrees with the truth table.

Part 4:  Xilinx project implementation.

Implement the simplified F3 from part 2 of this lab using the Xilinx software.  The VHDL code for both the project and the testbench will need to be writen.  The test bench will have to be sufficient enough to verify that the code is working properly

When completed, hand in the following deliverables (to the TA) as part of the formal report:
1.  Print out both sets of VHDL ensuring proper comments in the format used in Sample Project.
2.  For your function of four input variables, print out the simulated waveform traces (enough of the waveform so that all sixteen possible input combinations are shown), and show that the simulated waveform exactly matches the expected truth table.

Part 5.  K-Map Software

There are several software packages available that help with K-Map minimization.  One such package should be available as an icon on the desktop of this computer.  It is called "KMAP."  If there isn't, use explorer to go to the following directory c:\kmap and use the KMAP executable.  This particular package is Karnaugh Map 4.4.5 software.  For the price, it is a great little package.  A copy of it can be purchased for around $15.00 by clicking here or going to the links page.  Take some time to become familiarized with the software.  The worksheet has some required assignments to be done.