4 Boolean Algebra and Logic Simplification (重点
1 4 Boolean Algebra and Logic Simplification 重点
Contents Boolean operations and expressions Law and rules of boolean algebra ◆ DeMorgan’ s Theorems Boolean analysis of logic Circuits Simplification Using Boolean Algebra Standard Forms of boolean Expressions Boolean Expressions and Truth tables ◆ The Karnaugh Map Karnaugh Map SoP Minimization
2 Contents Boolean Operations and Expressions Law and Rules of Boolean Algebra DeMorgan’s Theorems Boolean Analysis of Logic Circuits Simplification Using Boolean Algebra Standard Forms of Boolean Expressions Boolean Expressions and Truth Tables The Karnaugh Map Karnaugh Map SOP Minimization
4-4 Boolean Anal ysis of Logic Circuits (逻辑电路分析) 1.Logic Circuit(逻辑电路图) D CDB (3+CD To derive the boolean expression for a given combinational logic circuit, begin at the left-most inputs and work toward the final output, writing the expression for each gate 2. Boolean Expression ⅹ=A(B+CD
3 4-4 Boolean Analysis of Logic Circuits （逻辑电路分析） 1.Logic Circuit (逻辑电路图） To derive the Boolean expression for a given combinational logic circuit , begin at the left-most inputs and work toward the final output , writing the expression for each gate. 2.Boolean Expression A ( B + C D ) C D B + C D X=A(B+CD)
4-4 Boolean Analysis of Logic Circuits 3. Truth table(真值表) Constructing the truth table from a logic expression (1) Determine the number of the input and output variables, and the number of the input variable possible ble combinations 2)Draw the truth table frame according to the input and output variables
4 4-4 Boolean Analysis of Logic Circuits 3. Truth Table （真值表） Constructing the truth table from a logic expression. (1) Determine the number of the input and output variables, and the number of the input variable possible combinations. (2) Draw the truth table frame according to the input and output variables
4-4 Boolean Analysis of Logic Circuits (3)List all of the input variable combinations of Is and0 s in a binary sequence(按序) (4)Fill the truth table. If the input variable combinations make the output 1, then place a 1 in the corresponding output column, otherwise lace a o
5 4-4 Boolean Analysis of Logic Circuits (3) List all of the input variable combinations of 1s and 0s in a binary sequence (按序）. (4) Fill the truth table. If the input variable combinations make the output 1, then place a 1 in the corresponding output column, otherwise place a 0