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