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 F1 F2 F3 F4 0 0 0 1 1 1 0 1 0 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. Problem 3.1. Do Problem 5.2, page 278 of the t extbook. (V) (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 trans fer characteristic shown in Fig. 1. This in-verter obeys the s tatic discipline for suitable choices of the voltages VOL, VIL, VIH , and VOH , (see Fig. 5.8 on page 250 of the textbook), and t h ose are such that NMH = 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 h igh (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 th an the threshold voltage. • The “on” resistance of t h e MOSFET is 100Ω. • The “off” resistance of the MOSFET is 100M Ω. 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 entr y of C in the corresponding truth table o f part a., find 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
View Full Document
Unlocking...