shared via CourseHero com This study resource was This study source was downloaded by 100000822808065 from CourseHero com on 04 05 2021 01 44 11 GMT 05 00 https www coursehero com file 62206357 DE 215docx Activity 2 1 5 Circuit Simplification DeMorgan s TheoremsIntroductionDespite all of the work done by George Boole there was still more work to be done Expanding on Boole s studies Augustus DeMorgan 1806 1871 developed two additional theorems that now bear his name Without DeMorgan s Theorems the complete simplification of logic expression would not be possible YXYX 2TheoremYXYX 1Theorem As we will seen in later activities DeMorgan s Theorems are the foundation for the NAND and NOR logic gates In this activity you will learn how to simplify logic expressions and digital logic circuits using DeMorgan s two theorems along with the other laws of Boolean algebra ProcedureUsing DeMorgan s theorems and the other theorems and laws of Boolean algebra simplify the following logic expressions Note the theorem law used at each simplification step Be sure to put your answer in Sum Of Products SOP form 1 F1 X YF1 X YTheorems 21 and 9 I then rewrote the equation w o AND symbols 2 F2 R S T U F2 RS T U Theroems 20 and 9 3 F3 M NF3 M N 2014 Project Lead The Way Inc Digital Electronics Activity 2 1 5 Circuit Simplification DeMorgan s Theorems Page 1 shared via CourseHero com This study resource was This study source was downloaded by 100000822808065 from CourseHero com on 04 05 2021 01 44 11 GMT 05 00 https www coursehero com file 62206357 DE 215docx Theorem 9 4 F4 W X Y Z F4 W X Y ZTheorems 20 and 9 5 F5 P Q R P Q RF5 P QR PQ R Theorems 21 and 96 F6 W X YZF6 W XYZLet s see how we would utilize DeMorgan s theorems to simplify a digital logic circuit 7 Write the UN SIMPLIFIED logic expression for the output Do Nothing in the logic circuit shown below X Y YZ X Y The output is call Do Nothing because that is exactly what the circuit does nothing yet it s a good example for learning about DeMorgan s theorems 2014 Project Lead The Way Inc Digital Electronics Activity 2 1 5 Circuit Simplification DeMorgan s Theorems Page 2 shared via CourseHero com This study resource was This study source was downloaded by 100000822808065 from CourseHero com on 04 05 2021 01 44 11 GMT 05 00 https www coursehero com file 62206357 DE 215docx 8 Using DeMorgan s theorems and the other theorems and laws of Boolean algebra simplify the logic expression Do Nothing Be sure to put your answer in Sum Of Products SOP form XY YZ 9 In the space provided draw an AOI circuit that implements the simplified logic expression Do Nothing For this implementation you may assume that AND OR gates are available with any number of inputs 2014 Project Lead The Way Inc Digital Electronics Activity 2 1 5 Circuit Simplification DeMorgan s Theorems Page 3 shared via CourseHero com This study resource was This study source was downloaded by 100000822808065 from CourseHero com on 04 05 2021 01 44 11 GMT 05 00 https www coursehero com file 62206357 DE 215docx Do Nothing I10 Re implement the circuit assuming that only 2 input AND gates 74LS08 2 input OR gates 74LS32 and inverters 74LS04 are available Draw this circuit in the space provided Do Nothing IIConclusion1 Draw the gate equivalent for DeMorgan s two theorems Theorem 1 X Y X Y 2014 Project Lead The Way Inc Digital Electronics Activity 2 1 5 Circuit Simplification DeMorgan s Theorems Page 4 shared via CourseHero com This study resource was This study source was downloaded by 100000822808065 from CourseHero com on 04 05 2021 01 44 11 GMT 05 00 https www coursehero com file 62206357 DE 215docx Powered by TCPDF www tcpdf org Theorem 2 X Y X Y2 How would you prove that the original Do Nothing circuit and the simplified version are equivalent You could create a truth table for them you could build the actual circuit in order to prove their similatiry 3 If each GATE cost 5 and you made 100 000 of the unsimplified units how much of the company s money did you waste on the unsimplified Do Nothing project The company wasted around 30 000 2014 Project Lead The Way Inc Digital Electronics Activity 2 1 5 Circuit Simplification DeMorgan s Theorems Page 5