Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2007 Homework 3 Handout S07 019 Issued 2 22 07 Due 3 2 07 Reading Chapter 5 Chapter 6 1 6 10 Exercise 3 1 The number of Boolean functions of one variable A is four F1 F2 F3 and F4 as it can be learned from the truth table given in Table 1 Then a How many different Boolean functions are there of 2 variables and of 3 variables b How many different Boolean functions are there of n variables A 0 1 F1 0 0 F2 0 1 F3 1 0 F4 1 1 Table 1 Truth table for the different Boolean Functions of one variable Exercise 3 2 Do Exercise 5 6 page 275 of the textbook parts a b and d Exercise 3 3 Do Exercise 6 2 page 322 of the textbook V Problem 3 1 Do Problem 5 2 page 278 of the textbook V Figure 1 Input Output transfer characteristic for inverter of Problem 3 2 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 Problem 3 2 An inverter has the input output transfer characteristic shown in Fig 1 This in verter obeys the static discipline for suitable choices of the voltages VOL VIL VIH and VOH see Fig 5 8 on page 250 of the textbook and those are such that N MH N ML Then a Give values of VOL VIL VIH and VOH that actually achieve the static discipline with the maxi mum positive noise margin b What is the noise margin you obtained Problem 3 3 For this problem consider the convention that a logical one corresponds to a high voltage level and a logical zero corresponds to a low voltage level Thus when the voltage vA associated with the Boolean variable A is high 3V A 1 When vA is low 0V A 0 The same relation holds with vB and B vC and C Assume also the following The high voltage level is much greater than the threshold voltage The on resistance of the MOSFET is 100 The off resistance of the MOSFET is 100M Then for each circuit in Fig 2 a Generate a truth table which shows how the variable C associated with vC depends on the inputs A associated with vA and B associated with vB b For each particular entry of C in the corresponding truth table of part a nd the value of the output voltage vc Figure 2 Circuits for Problem 3 3 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
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