《数字电》英文版 chapter3

Combinational logic circuits Chapter 3 Analysis design

Combinational logic circuits Chapter 3 Analysis & design

Definition of combinational logic Combinational logic n fur nction Let x be the set of all input variables,X={X0,×1,……×n Let y be the set of all output variables, y=tyo, y1,.,ymy a The combinational function f, operated on the input variable set X, to produce the output variable set y a the output is related to the input as y=F(X)>Yi=F(X0,X1,…×X)

Definition of combinational logic Let X be the set of all input variables , X={X0 , X1 , ……, Xn } Let Y be the set of all output variables , Y={Y0 , Y1 , ……, Ym} Y=F(X) >> Yi=F(X0 , X1 , ……, Xn )  The combinational function, F, operated on the input variable set X, to produce the output variable set Y.  The output is related to the input as Combinational logic function (F) X0 Xn Y0 Ym

Definition of combinational logic Combinational logic n function(F) a Logic circuits without the feedback from output to input a Logic circuits constructed from a functional completely gate set, contain no memory unit

Definition of combinational logic  Logic circuits without the feedback from output to input  Logic circuits constructed from a functionally completely gate set, contain no memory unit Combinational logic function (F) X0 Xn Y0 Ym

Analyze a combinational logic circuit Logic diagram a Convert logic diagram to switching equation Switching equation a Simplify the expression a derive the truth table from Simplify equation the simplified switching equation Construct truth table a Give the pertinent statement f the circuit (function\ design Function statement

Analyze a combinational logic circuit Function statement Construct truth table Simplify equation Switching equation Logic diagram  Convert logic diagram to switching equation  Simplify the expression  derive the truth table from the simplified switching equation  Give the pertinent statement of the circuit (function\design)

Design a combinational logic circuit Problem statement a Develop a proper Truth table Construction statement of the problem 口 Based on the prob|em switching equations written statement, construct truth table that clearly established the Equations simplified relationship between the nput and output variables Logic diagram drawn Logic circuit built

Design a combinational logic circuit Logic circuit built Logic diagram drawn Equations simplified switching equations written Truth table Construction Problem statement  Develop a proper statement of the problem  Based on the problem statement, construct truth table that clearly established the relationship between the input and output variables

Design a combinational logic circuit a Determine the input variables and output variables that are involved Problem statement Assign mnemonic or letter or number symbols to each variable a Determine the size of the truth Truth table table Construction Construct a truth table containing all of the input variable combination By careful reading of the problem statement determine the combinations of input that cause a given output to be true

Design a combinational logic circuit ◼ Determine the input variables and output variables that are involved ◼ Assign mnemonic or letter or number symbols to each variable ◼ Determine the size of the truth table ◼ Construct a truth table containing all of the input variable combination ◼ By careful reading of the problem statement determine the combinations of input that cause a given output to be true Truth table Construction Problem statement

Example Conveyor system 口 Elements a Two operator ■ Materia ■ Inter| ock switch ■ Motor a put conveyor into action >>the motor is turning on a Either of two operators is in position The interlock switch is closed a Material must be present

 Elements ◼ Two operator ◼ Material ◼ Interlock switch ◼ Motor  put conveyor into action >> the motor is turning on ◼ Either of two operators is in position ◼ The interlock switch is closed ◼ Material must be present Example : Conveyor system

Example: Conveyor system 4 input variables a=1, operator 1 is in position b=1, operator 2 is in position a m=1, material is present s=1. interlock switch is closed 口1 output variable aM is the signal to turn the motor off or on a M=1, the motor is turning on

 4 input variables ◼ a=1, operator 1 is in position ◼ b=1, operator 2 is in position ◼ m=1, material is present ◼ s=1, interlock switch is closed.  1 output variable ◼ M is the signal to turn the motor off or on ◼ M=1, the motor is turning on Example : Conveyor system

Example: Conveyor system a bm s m a bms M 00000 10000 0001 0 10010 00100 1010 0 00 10111 00 11000 0000 01 00001 1 1 110 111 011 0 001

a b m s M 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 a b m s M 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 Example : Conveyor system

Example: Nasn syStem a Elements Two on-line computers a One redundant computer a Three self-checking diagnostics components a The control logic to connect or disconnect the computers A warning allow the third computer to come on-line aa warning invoke the emergency procedures

 Elements ◼ Two on-line computers ◼ One redundant computer ◼ Three self-checking diagnostics components ◼ The control logic to connect or disconnect the computers. ◼ A warning, allow the third computer to come on-line. ◼ A warning, invoke the emergency procedures. Example : NASN system