ECE380_Chapter4(1).pdf - INTRODUCTION TO DIGITAL LOGIC ECE 380 Optimized Implementation of Logic Functions Jacob Chakareski Department of Electrical and

# ECE380_Chapter4(1).pdf - INTRODUCTION TO DIGITAL LOGIC ECE...

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INTRODUCTION TO DIGITAL LOGIC ECE 380 Optimized Implementation of Logic Functions Jacob Chakareski Department of Electrical and Computer Engineering Jacob Chakareski: ECE 380 Optimized Implementation of Logic Functions 2 Synthesis of Logic Functions Implementation via Sum of products form Product of sums form Algebraic manipulation to minimize cost Automatic optimization via CAD tools Learning objective: Karnaugh maps Jacob Chakareski: ECE 380 Optimized Implementation of Logic Functions 3 Function Synthesis Example f (x 1 , x 2 , x 3 ) = m (0, 2, 4, 5, 6) Jacob Chakareski: ECE 380 Optimized Implementation of Logic Functions 4 Algebraic Simplification Iteratively apply combining identity f = m 0 + m 2 + m 4 + m 5 + m 6 = x 1 x 2 x 3 + x 1 x 2 x 3 + x 1 x 2 x 3 + x 1 x 2 x 3 + x 1 x 2 x 3 = x 1 x 3 + x 1 x 2 x 3 + x 1 x 3 (m 4 =m 4 +m 4 : T3) = x 3 + x 1 x 2 Simplify by grouping minterms _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Jacob Chakareski: ECE 380 Optimized Implementation of Logic Functions 5 Group Suitable Minterms x 1 x 2 x 3 m 0 0 0 0 m 2 0 1 0 m 4 1 0 0 m 6 1 1 0 x 1 x 2 x 3 m 4 1 0 0 m 5 1 0 1 Jacob Chakareski: ECE 380 Optimized Implementation of Logic Functions 6 Karnaugh Map: Table & Cells x 2 (a) Truth table (b) Karnaugh map 0 1 0 1 m 0 m 2 m 3 m 1 x 1 x 2 0 0 0 1 1 0 1 1 m 0 m 1 m 3 m 2 x 1 Minterms in adjacent cells can be combined 