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AOI Logic Analysis Fill in your notes Digital Electronics There are 2 ways to analyze Truth Table → Equation Technique Given A Logic Circuit . . . • Extract truth table • Derive logic expression Equation → Truth Table Technique These are 2 ways you can analyze a logic circuit Given A Logic Circuit . . . • Extract logic expression • Derive truth table 2 Truth Table → Equation Technique The Process a) Add test-points at the output of every gate. b) Add a column to the truth table for every testpoint. c) Working from the inputs to the output, complete the truth table for each test-point, ultimately ending at the circuit’s output. d) From the completed truth table, identify the Minterms from the truth table anywhere the output is one. e) Using the extracted Minterms, write the Sum-Of3 Products logic expression. Truth Table → Equation Process Walk-Thru The next slides will show how to figure out the logic expression for the output F1 . 4 Truth Table → Equation Process Walk-Thru : Step (a) a) Add test-points at the output of every gate. TP1 TP2 TP3 TP5 TP4 Write down what each test point really means on the drawing TP1= X inverted = X TP2= XY TP3=XYZ TP4=Y TP5=XY 5 Truth Table → Equation Process Walk-Thru : Steps (b) & (c) b) Add a column to the truth table for every test-point. c) Working from the inputs to the output, complete the truth table for each test-point, ultimately ending at the circuit’s output. Notice that TP1 is exactly the opposite of X X Y Z F1 TP1 TP2 TP3 TP4 TP5 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 TP5 = X and TP4 If both X and TP4 are 1, then TP5 is also a 1 6 Truth Table → Equation Process Walk-Thru : Steps (d) & (e) d) From the completed truth table, identify the Minterms from the truth table anywhere the output is one. X Y Z F1 TP1 TP2 TP3 TP4 TP5 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 XY Z 0 1 1 1 1 1 1 0 0 X Y Z 1 0 0 1 0 0 0 1 1 X Y Z 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 Write down the equations e) Using the extracted Minterms, write the Sum-OfProducts logic expression. F1 X Y Z X Y Z X Y Z 7 Example #1: Circuit Analysis Example Here is another, do this one Analyze the logic circuit shown below to determine the circuit’s truth table. Using the truth table, derive the logic expression for the output F2. You should try to solve this yourself and fill in the next slide BEFORE you look at the answer coming up! 8 Example #1: Circuit Analysis Solution TP1 a) TP2 TP3 TP4 TP5 b) & c) d) B C F2 TP1 TP2 TP3 TP5 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 XY Z 0 1 0 1 1 1 0 1 1 XY Z 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 XY Z e) e) TP4 A F2 X Y Z X Y Z X Y Z 9 Equation → Truth Table Technique The Process This is the OTHER way to analyze circuits a) Working from the inputs to the output, write the cumulating logic expression at the output of each gate concluding with the expression for the circuit’s output. b) Using the circuit’s output logic expression, derive the circuit’s truth table. 10 Equation → Truth Table Technique Process Walk-Thru Analyze the logic circuit shown below to determine the logic expression for the output F1. Using the logic expression, derive the circuit’s truth table. 11 Equation → Truth Table Technique Process Walk-Thru : Step (a) a) Working from the inputs to the output, write the cumulating logic expression at the output of each gate concluding with the expression for the circuit’s output. X XY XY Z Y XY Z XY X Y 12 Equation → Truth Table Technique Process Walk-Thru : Step (b) b) Using the circuit’s output logic expression, derive the circuit’s truth table. F1 X Y Z X Y X Y Z F1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 If you look at the picture of the circuit you can write what the equation is XY Z X Y 13 Example #2: Circuit Analysis Example Analyze the logic circuit shown below to determine the logic expression for the output F1. Using the logic expression, derive the circuit’s truth table. Do this one on your own 14