Laboratory Two Simplification of Logic Circuits Basic Concepts 1. Logic circuits realize Boolean expressions. 2. Logic circuits may be simplified by applying Boolean postulates and theorems. 3. Equivalent logic circuits have the same truth table. Note: Steps marked with (Pre) below, indicate prelab work to be done and recorded in your laboratory notebook before coming to lab. Task One: Expressions from Circuits Consider the logic circuits shown to the right. 1. (Pre) Draw circuits F1 through F6 in your lab notebook, and mark pin numbers next to each input and output terminal. [For the 4-input AND (which we don't have), use the 7420 NAND, followed by a 7404 inverter.] See: SSI data sheet. 2. (Pre) Derive a Boolean expression for each circuit Fi in your notebook, showing your steps of calculation. 3. (Pre) Draw a theo e ical truth table for the Fi, in terms of inputs A, B and C (for Fr t3 and F4, just use A). (To save space, consider drawing one long horizontal table showing the various terms of the Fi in columns after A, B and C.) 4. (Pre) Simplify your expression for the Fi using the Boolean algebra postulates and theorems given in the notes, stating which property(ies) you are using (for example, you may want to write the "absorption" or one of the "identity" properties). Draw a simplified circuit for each Fi. 5. In the lab, build the original and simplified circuits for F1 through F4 and check to see if they behave the same (flip the switches and watch how the output lights go on and off for each circuit). Do not disassemble any of your Fi circuits. 6. Finally, build the original and simplified circuits for F5 and F6, using your wired circuits F1 through F4 as a starting point. Record experimental truth tables for F5 and F6.Task Two: Circuits from Expressions 1. (Pre) Draw logic circuits which exactly reproduce F7 through F10 shown at right (do not attempt to simplify or rewrite the expressions). You may use any gates that are available in the Xilinx library (no pin numbers are required here, by the way). ACBCBAFCBAABCFCACBBAFCBBABAF+++=+=+++=++=)())()(()(109872. (Pre) Draw the theoretical truth table for the Fi in terms of A, B and C. 3. (Pre) Next, simplify the Fi using the techniques learned in Task One. (These problems will require multiple application of the Boolean theorems.) Draw the resulting simplified circuits in your notebook. 4. Enter the logic circuits for both the original and simplified expressions for the Fi into Xilinx's Schematic Editor. Employ the Functional Simulation and design an arrangement to test all eight circuits simultaneously and prove that the original and simplified circuits are equivalent. From your simulation results, record an experimental truth table in your lab notebook for the Fi. How do these results compare with your theoretical