Electronic Labs_4 - (Amiga ~63 1—(Evb Fig 26-3 8 2...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (Amiga ~63 +1—(Evb) Fig. 26-3 8/ 2. a)Re‘ferring to the output _of_ the circuit of Fig. 26-3 as ~\.¥=(A+B)(B+C)+A(C+D), is it possible to simplify any part of the equation, and if so, which part? 0 — _ AB...rl:.l\..93§l§l3.fl:§._..i...A§~.._-.LA.D ............ It ispossible to simplify the expression (A+B)(B+C). lE/ b) Simplify the expression (A+B) (B+C) using Boolean algebra and state the ,full simplified equation for the circuit of Fig. 26-3. (A+B)(B+C) =AB+AC+BB+BC [Algebraic expansion (Distrib— fi’ utiue Law)] =AB+A C+B+BC — [BB=B(Identity)] T-‘AB+AC+B(1)+BC [B=B_(r) (Identity ) ] =B(1)+AB+BC+AC [Rearrange terms (Commuta- tive Law)] =(B-1+AB+BC)+AC [Group B terms (Associative Law)] Boolean Algebra 26-3 =‘Bl(rlj+A’+C')fl-AC [Factor out B (Distributive ' ‘ ' Law)] ' eB‘a )‘+AC [B(1+A+C)=B(l ) (Identity)] =B+AC [B(1)=B (Identity)] «’\ Therefore: (A+B)(B+C)+X(5+D)fi§}lflfi@z(5+D). [2/ c)Ca.n the circuit of Fig. 26-4 be used to ' iinplement the simplified logic equation Y=B+AC+' A(C+D)? Xes, the gate o_ut£uts are as follows: gate A is C+D; gate_(,;is A(C+D),' gate B is AC; and gate D is B+A C+A(C +D). Fig. 26-4 C! d) Compare the circuits of Fig. 26-3 and 26-4. How many and what type of logic gates have been eliminated from the circuit by simpli- fication using Boolean algebra? r'} _ '-_,"‘._ ." C Two OR gates have been eliminated. Objective B. Determine that DeMorgan’s theorems define the dual gating functions of the basic NAND and NOR gates and verify that these theorems can be applied to complex logic circuits. Preparatory Information. DeMorgan’s theorems re- late to the dual gating functions 'of the basic NAND and NOR gates. This provides a powerful tool in solving Boolean equations since the dual for each function can be substituted directly in an equation for the basic function. Additionally, because the duality exists for gates with any number of inputs, DeMorgan’s theorems are valid for equations with any number of variables and for equations having complex terms that have the basic form. DeMOrgan’s theorems are: (1) A+B=“A‘-}"3' (2) A-B=A+B For any number of variables, the theorems take the form: ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern