PHYS 375: Homework assignment 6due date: May 9, 2008.1. Prove the following Boolean equations.(a) x + y.x = x(b) x + ¯x.y = x + y(c) x + (y.z) = (x + y).(x + z)(d) ¯u = (¯c.(w + r)) is equivalent to ¯u = c + ¯w.¯r2. Consider the Karnaugh map given in Figure 1. Write down the Boolean ex-pression associated to this map.Figure 1: Karnaugh map associated to exercise 2.3. Implement the following equation S = A.¯B.C + B.¯D using only two-inputsNOR logical gates.4. The attached document (HW6 data 74ls151.pdf) contains the characteristicsof the 74LS151 chip used in Lab. 12.(a) From the truth table provided in this sheet, prove that the sequence usedfor D0-D7 switch in the lab is proper for generating prime number (hereprime means 2,3,5,7).1(b) Write down which combination of A0, A1, A2 yield a prime number.5. In Lesson 12 handout, a slide on Karnaugh map presents a p ossible way ofgenerating the month number (1 to 12) corresponding to Jan to Dec.(a) We seek to generate the month numbers by using four inputs. Why four?(b) Retrieve the Karnaugh map shown. Knowing that to each valid monthnumber (that is an integer between 1 and 12) we associate either T or Fdepending on the number of days in the month (T=31 days and F=not 31days).(c) Write down the expression associated to this map (carefully explain howyou come to this expression since the solution is
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