{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW 2 - 1 a Label the inputs so that the output is a.c(a AND...

This preview shows pages 1–3. Sign up to view the full content.

1. a) Label the inputs so that the output is a.c (a AND c) b) Using only AND, OR, NOT gates, draw the combinational logic network for h which precisely corresponds to the following expression. Use fanout as appropriate, but do not simplify . h(w,x,y,z) = (w + x' + y) + 0 y' + (x' z + w')' Assume that complemented inputs are available; i.e., assume that for each variable w, x, y, z, both the variable and its complement are available as inputs: w, w', x, x', y, y', z, z'. 2. a) Consider the following 3-input XOR gate z a b c Write the formula for z in terms of AND, OR, and NOT. b) If any ONE of a, b or c is inverted, what is the new z ? Show that this new z remains the same irrespective of which input you choose to invert. This Boolean expression corresponds to the output of a different type of gate; what is this gate called? c) What happens to z if they are all inverted at the same time? 3. a) A literal is a variable in its true or complemented form. Simplify the following functions such that there are minimum total literals. Write the Boolean identity you are using at each step. Use no more than 8 steps per item. i) ( , , ) ( )( )( ) f x y z x y x y z x y z ± ± ± ± ± ii) ( , , , ) f w x y z x xyz xyz xy wx wx ± ± ± ± ± iii) f(A,B,C,D) = (AB + A’B’)(C’D’ + CD) + (AC)’

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
iv) f(X, Y, Z) = X+Y(Z+(X+Z) ) b) (i) Use less than 6 steps to prove: a' + wam' + wm + v'wz = a' + w (ii) State and prove the dual of the theorem in part (i). Align the dual proof
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern