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EE 110 Spring 2018

Homework 03

D. Willie

Homework is due, Wed Feb 7 in class. 25% credit off before midnight (scan and email). After

midnight no credit! 5 problems, 100 points total, 102 points max.

Write your name, the assignment name, and the date at the top of the first page of each

assignment. Staple multiple pages together. Number all problems and put them in order in your

assignment. Please write clearly and draw a box around numerical answers. You will not get

credit if your work is difficult to follow or the answer in a box is not easily seen. You will not get

full credit if these directions aren?t followed.

1. (7 pts each) Use the Boolean Postulates and Theorems (table 2.2 of the

textbook) to simplify the following expressions as far as possible. Show and justify

each step by citing the theorem or postulate used.

a.

?(?, ?, ?, ?) = ??? ¯¯¯¯¯¯¯¯¯¯¯¯¯

?¯ ?¯ ?¯ ??

b.

f (W , X,Y,Z) ? (W ?Y ? Z)(X ?Y)(W ? X ? Z)(X ?Y)(X ?Y ? Z)

c.

f (A,B,C) ? (A ? B)(A ? AB)(A ? B ? ABC) ? (A ? B)(A ? C)

2. (7??pts each) Given each function shown, take its complement and then use

DeMorgan?s theorem to eliminate all group complements from your final expression.

?? the complement simply means to place a bar over the entire expression.)

(Taking

a.

X(Y ? Z(Q ? R))

b.

X ? Y(Z ? QR)

?? c.

(A ? BC)(A ? DE)

3. (5??pts each) Given the following logic circuit

??

a. Write the Boolean equation for f (A,B,C,D) from the above diagram.

b. Write the complete truth table for f (A,B,C,D) .

c. Find the minimum sum-of-products (SOP) expression for f (A,B,C,D) .

Show your steps and justify

your answer.

??

d. Draw the logic circuit equivalent

to the minimum SOP expression you

??

found in part (c).

??

4. (5 pts each) Given the following shorthand canonical SOP expression:

f (x, y, z) ? ? m(0,2, 3,6, 7)

a. List the complete truth table for f (x, y, z) .

b. Express f (x, y,??z) in fully expanded SOP canonical form.

??

c. Express f (x, y, z) in shorthand POS canonical form.

??

d. Express f (x, y, z) in fully expanded POS canonical form.

??

5. (5 pts each) Given the following shorthand canonical POS expression:

??

f ( p,q,r, s) ? ? M (1, 3, 4, 7,11,12,14)

a. List the complete truth table for f ( p,q,r, s).

b. Express ??

f ( p,q,r, s) in fully expanded POS canonical form.

??

c. Express f ( p,q,r, s) in shorthand SOP canonical form.

??

d. Express f ( p,q,r, s) in fully expanded SOP canonical form.

??

??

…

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