Name:_____________ Date:_______ Score:_____ Activity 2.1.4 AOI Logic Analysis Introduction What does this circuit do? Does the circuit that I designed work? If you are able to analyze AOI logic circuits, you will be able to answer these questions. The first question frequently comes up when you need to determine the functionality of a previously designed circuit. The second question will always need to be answered whenever you design a new logic circuit. When you analyze an AOI logic circuit, you can use one of two techniques. With the first technique, you determine the circuit’s truth table from which the output logic expression is derived. With the second technique, the order is reversed. The circuit’s logic expression is determined. The truth table is then derived using this expression. In this activity you will learn how to analyze AOI logic circuits to determine the circuit truth table and output logic expression. Equipment Paper and Pencil Calculator Procedure Let’s start by analyzing the relatively simple AOI logic circuit shown below. You will use the technique where you first extract the truth table and then use the truth table to derive the output’s logic expression. 1. Using the test points that have been assigned (TP1-TP4), complete the following truth table. TP 1 TP3 X Y 0 0 0 1 1 0 1 1 F1 TP1 TP 2 TP 4 TP2 TP3 TP4 2. Using the truth table, write out the Minterms for every location that contains a (1) in the F1 column. 3. Using the Minterm(s), write the logic expression for the output F1. Re-analyze the simple AOI logic circuit using the technique where you first extract the logic expression for the output and then use the logic expression to derive the truth table. 1. Using the circuit diagram below, write the logic expression at the output of each gate until you reach the output of the circuit. 2. Using the logic expression, complete the truth table shown below. X Y 0 0 0 1 1 0 1 1 F1 How do the logic expressions and truth tables obtained from the two techniques compare? Are they the same? They should be. If they are not, review your work and correct any mistakes. Let’s analyze a more complex circuit. Complete the following steps for the three input AOI logic diagram shown below. 1. Using the analysis technique where you first extract the truth table and then use it to derive the output’s logic expression, analyze the circuit. Record your results below. R S T 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 F2 F2 = _______________________ 2. Now, using the analysis technique where you first extract the logic expression for the output and then use it to derive the truth table, analyze the circuit. Record your results below. R S T 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 F2 F2 = _______________________ 3. How do the truth tables obtained from the two techniques compare? Are they the same? They should be. If they are not, review your work and correct any mistakes. 4. How do the logic expressions obtained from the two techniques compare? Are they the same? They are NOT the SAME, but they are EQUAL. In later activities we will learn how to use Boolean algebra to simplify logic expressions like these and prove that they are equal. Conclusion 1. In your own words, describe the process used to analyze a logic circuit where you first extract a truth table and then derive the logic expression. 2. Again, in your own words, describe the process used to analyze a logic circuit where you first extract the logic expression and then derive the truth table. 3. Did you find one of the processes easier than the other? Which one and why? 4. What is the difference between two logic equations being equal versus two logic equations being equivalent?