Unit IV Fundamentals of Logic Design by Roth and Kinney

4.1 Conversion of English Sentences to Boolean Equations Logic Design Problems –Mary watches TV if it is Monday night and she has finished her homework. F=1 if “Mary watches TV” is true, otherwise F=0. A=1 if “it is Monday night” is true; otherwise A=0. B=1 if “she has finished her homework” is true; otherwise B=0. –F is “true” if A and B are both “true”, then F=AB.

Another Example (p.95) The alarm wil ring iff the alarm switch is turned on and the door is not closed, or it is after 6pm and the window is not closed. –Let Z be associated with “the alarm will ring.” –Let A be associated with “the alarm switch is on.” –Let B’ be associated with “the door is not closed.” –Let C be associated with “it is after 6pm.” –Let D’ be associated with “ the window is not closed.” With this association of variables, Z = AB’ + CD’. A circuit can be established as shown on page 95.

4.2 Combinational Logic Design Using a Truth Table Page 96 illustrates a Truth Table. Take the 1’s and AND them: –f= A’BC + AB’C’ + AB’C + ABC’ + ABC This can be simplified: –f = A’BC + AB’ + AB = A’BC + A + A + BC (4- 2) –The resulting circuit is shown on page 96.

Implementing f in terms of the 0’s Take the 0’s and AND them: –f = (A+B+C)(A +B + C’)(A + B’ +C) Simplification: –F = (A+B)(A+B’+ C) = A + B(B’+C) = A + BC Equation (4-4) Another way: –Write f’ as a sum of products and then complement the result. –f’ = A’B’C’ + A’B’C + A’B C’ –Then f = (A + B + C)(A + B + C’)(A + B’ + C)