6 002 CIRCUITS AND ELECTRONICS The Digital Abstraction Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Review z Discretize matter by agreeing to observe the lumped matter discipline Lumped Circuit Abstraction zAnalysis tool kit KVL KCL node method superposition Th venin Norton remember superposition Th venin Norton apply only for linear circuits Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Today Discretize value Digital abstraction Interestingly we will see shortly that the tools learned in the previous three lectures are sufficient to analyze simple digital circuits Reading Chapter 5 of Agarwal Lang Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 But first why digital In the past Analog signal processing R1 V0 R2 V1 and V2 might represent the outputs of two sensors for example V1 V2 By superposition V0 R2 R1 V1 V2 R1 R2 R1 R2 If R1 R 2 V1 V2 V0 2 The above is an adder circuit Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Noise Problem t add noise on this wire Receiver huh noise hampers our ability to distinguish between small differences in value e g between 3 1V and 3 2V Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Value Discretization Restrict values to be one of two HIGH LOW 5V 0V TRUE FALSE 1 0 like two digits 0 and 1 Why is this discretization useful Remember numbers larger than 1 can be represented using multiple binary digits and coding much like using multiple decimal digits to represent numbers greater than 9 E g the binary number 101 has decimal value 5 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Digital System sender noise VN VS VR VN 0V receiver VS VR 5V 0 1 0 HIGH 0 1 0 5V t 2 5V 0V LOW 0V t 2 5V With noise VS VN 0 2V 0 1 0 5V 0 1 0 0 2V t t 2 5V VS 2 5V t 0V Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Digital System Better noise immunity Lots of noise margin For 1 noise margin 5V to 2 5V 2 5V For 0 noise margin 0V to 2 5V 2 5V Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Voltage Thresholds and Logic Values 5V 1 1 sender 0 1 2 5V receiver 0 0 0V Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 But but but What about 2 5V Hmmm create no man s land or forbidden region For example 5V 1 sender 3V 2V 0 1 VH forbidden region receiver VL 0 0V 1 V 0 0V H 5V V L Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 But but but Where s the noise margin What if the sender sent 1 VH Hold the sender to tougher standards 5V 1 V 0H 1 V IH sender V IL 0 receiver 0 V 0L 0V Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 But but but Where s the noise margin What if the sender sent 1 VH Hold the sender to tougher standards 5V 1 V 0H 1 sender Noise margins V IH receiver V IL 0 0 V 0L 0V 1 noise margin V V IH 0H 0 noise margin VIL V 0L Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 5V V 0H V IH V IL V 0L 0V 5V V 0H V IH V IL V 0L 0V 0 1 0 1 sender t 0 1 0 1 receiver t Digital systems follow static discipline if inputs to the digital system meet valid input thresholds then the system guarantees its outputs will meet valid output thresholds Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Processing digital signals Recall we have only two values 1 0 Map naturally to logic T F Can also represent numbers Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Processing digital signals Boolean Logic If X is true and Y is true Then Z is true else Z is false Z X AND Y X Y Z are digital signals 0 1 Z X Y Boolean equation X Y AND gate Z Truth table representation X Y Z 0 0 1 1 0 1 0 1 0 0 0 1 Enumerate all input combinations Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 6 002 Fall 2000 Lecture 4 Combinational gate abstraction Adheres to static discipline Outputs are a function of inputs alone Digital logic designers do not have to care about what is inside a gate Cite as Anant Agarwal and Jeffrey Lang course …
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