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LOGICSIM
2.3 Equipment Required: 2.3.1 Software simulation: The Logisim software package is installed on every PC in the lab. 2.3.2 Hardware implementation: The following equipment are needed to perform all the procedures: IC Training Kit Jumper wire kit 1x 7404 TTL HEX INVERTER GATE 1x 7411 TTL TRIPLE 3-input AND GATE 1x 7432 TTL QUAD 2-input OR GATE 3x Toggle Switches 1x Carbon-film Resistor (47022) 1x LED 2.4 Prelab: It is recommended that you review how to simplify Boolean functions using Boolean algebra and K-maps. 2.5 Software Simulation: 2.5.1 Login into one of the PCs in the lab using your user name and password. 2.5.2 Double click on the logisim-win-2.7.1 icon on the desktop of the computer. 2.5.3 In the area below, use basic gates to draw the logic diagram of the Boolean function: F=X' Y' Z+X' YZ+X Y'. If necessary, have your TA to check your circuit Combinational Analysis O Х 0 File Edit Project Simulate Window Help Inputs Outputs Table Expression Minimized 0 F 0 x 0 0 0 0 1 у 0 0 1 1 0 0 Z 0 1 0 1 0 1 1 0 1 1 1
2.5.4 As you did in Lab (1), enter your circuit into Logisim 2.5.5 Use the poke tool (chy to simulate your circuit and fill in the following truth table. F X 0 Y 0 Z 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 2.5.6 Save you circuit under the name Lab2original. You will need it again during this lab. - 19 - 2.5.7 Now, simplify the function using Boolean algebra. Show all the simplification steps and write the most simplified form in the following area. Have your TA to check your work. F = XYZ + XYZ + XY F = XZ(Y + Y) + XY F = Āz (1) + X7 F = XZ + XY
2.5.8 Simplify the function using the K-map and ensure that you get the same simplified expression as the one resulted from the Boolean algebra simplification. Use the following area to draw your K-map and write the most simplified expression Z Z 1 XY 0 = F = XYZ + XYZ + XYZ + XYZ F = ÃZ (7 + Y) + X7 (7 + 2) F = (1) + X7 (1) F = XZ + XY F + ХҮ = 0 1 XY 0 0 ХҮ 1 2.5.9 In the area below, use basic gates to draw the logic diagram of the simplified expression. 0 Х > Combinational Analysis File Edit Project Simulate Window Help Inputs Outputs Table Expression Minimized OIX 0 Y X Y N F ON O 0 1 х 0 0 0 0 1 1 1 1 OOOO OOOO 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 Build Circuit
2.5.10 Start a new Logisim project and enter the circuit you drew for the simplified expression into it. 2.5.11 Use the poke tool (b) to simulate your simplified circuit and fill in the following truth table. The table should be identical to the one of the original circuit, in step 2.5.5 F X 0 0 Z 0 0 Y 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 2.5.12 Count the number of gates in your original circuit and the number of gates in the simplified one. Consider the three-input AND gate to be equivalent to 2 two-input AND gates. How many gates could you save by simplification? 3 2.5.13 Now, let's use Logisim to carry out the simplification you did manually on steps 2.5.7 and 2.5.8 2.5.14 From the File menu, select Open Recent and click on your original file, Lab2original. 2.5.15 From the Project menu, click on Analyze Circuit
File Edit Project Simulate Window Help Add Circuit... Load Library Unload Libraries... AND US ma + Wir Gat XAQAAAAAAX Move Circuit Up Move Circuit Down Set As Main Circuit Remove Circuit Revert To Default Appearance View Toolbox View Simulation Tree Edit Circuit Layout Edit Circuit Appearance Analyze Circuit Get Circuit Statistics + Ple: Arit Options.. 2.5.16 The Combinational Analysis window will show up D х ► Combinational Analysis File Edit Project Simulate Window Help Inputs Outputs Table Expression Minimized < Remove Move Up Move Down Rename Add Build Circuit 2.5.17 Go to the Expression tab, you will see your original expression as in point 2.5.3.
2.5.17 Go to the Expression tab, you will see your original expression as in point 2.5.3. х Combinational Analysis File Edit Project Simulate Window Help Inputs Outputs Table Expression Minimized Output: F X¥2 + XYZ+XY -X Y Z + X Y Z + x -Y Clear Revert Enter Build Circuit 2.5.18 Go to the Minimized tab, you will see the K-map simplification of the Boolean function and the simplified expression. It should be identical to the one you obtained in steps 2.5.7 and 2.5.8.
2.5.23 Go to Logisim main window. You will find that the original circuit is replaced by the simplified one. Ensure that it is the same as the simplified circuit you generated before. Logisim: main File Edit Project Simulate Window Help VA C D D X 0 Y + 1 x Lab2original main - Wiring - Gates - Plexers Arithmetic - Memory - Input/Output - Base 2.5.24 After you are done, remember to back up your work onto a USB drive or to email it to yourself for future usage. 2.6 Hardware Implementation: 2.6.1 Collect the components necessary to implement the original circuit, as listed in Section 2.3. Noticethat you have drawn the logic diagram of the circuit in step 2.5.3. 2.6.2 As you did in Lab (1), plug each IC chip into the IC Training Kit. 2.6.3 Check the datasheet of each IC and according to the pin-out diagram of the IC chips, wire the logic circuit. Insert your wires carefully and avoid any loose connection. 2.6.4 Be sure to connect the supply voltage and ground lines (5V and OV) to all chips. 2.6.5 Once all connections have been done, turn on the power switch of the IC Training Kit. 2.6.6 Use the three switches for X, Y, and Z to enter all possible input combinations in order to fill in the truth table below: Y X' Y' Z XYZ XY F X 0 0 Z 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 باها 1 1 1
2.6.10 After finishing the experiment, turn the power OFF, disconnect the wires, take out all IC chips from the trainer, put back everything you have used and clean your table. 24- 2.7Questions: Practice Simplification of Boolean Functions For each of the following Boolean functions it is required to do all of the following and include your work onto the report. Draw the logic diagram corresponding to each function Simplify the function manually using Boolean algebra and K-map Enter the original logic diagram onto Logisim. Then, using the Combinational Analysis window, ensure that the simplification you did is correct. Snapshots from Logisim should be included in your report F= A'B'C' + A'B' C + ABC F= A' (BC+B C') + A B C +B C')