~~~Name:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~    Name:                                                  

 

ECE 201Spring 03 Quiz2                   Page 1 of 6

 

For each of the following circle ALL CORRECT ANSWERS. There may be one, zero or many correct answers.  If none of the answers are correct, circle nothing.  Each possible answer in the multiple choice will be graded separately-credit will be given for correctly circling or not circling each choice.

soltest2-1.png

1.)  Which of the following minterms of F are represented in the 4-variable K-map shown above? (8pts)

 

a.) w'x'y'z'

 
c) w'xy'z
  e.)  w'xyz
g.)wx'y'z
b.) w'x'yz  
d.) wx'y'z'
    
f.)  wxy'z'
h.)wxyz

SOLUTION: Find the 1's; a,c,d,f,g

 
2.) Which of the following maxterms of F are represented in the 4-variable K-map shown above? (8pts)

 

a) w'+x'+y'+z'

c.) w'+x+y'+ze.)w'+x+y+z g.)w+x'+y'+z

 

b.) w'+x'+y+z
d.) w+x'+y'+z'
f.)w+x+y'+z'
h.)w+x+y+z

 

SOLUTION: Find the 0's - Remember, primed variables are 1 and

unprimed are 0; a d, and f

3.) Which of the following is an essential prime implicant in the minimum SOP representation of F in the 4 variable K-map shown above? (8pts)

 

a.) wy' b.) wz' c.) x'y' d.)x'z'

e.) y'z

f.) yz'
g.) wx'y' h.)w'x'y'z'

 

4.) For the function shown in the k-map above, which of the following is a prime implicant of F? (8 pts)

 

a.) wy'

b.) wz'
c.) x'y'
d.)x'z'
e.) y'z
f.) yz'
g.) wx'y' h.)w'x'y'z'

 

5.) For the 4 variable K-map shown above, what is :(8 pts)

a.) A minimal sum-of-products expression for F'

 

(Group 1s) Any of:

F(MSOP)= y'z + yz'+x'z' + wy'

F(MSOP)= y'z + yz'+x'z' + wz'

F(MSOP)= y'z + yz'+x'y' + wy'

F(MSOP)= y'z + yz'+x'y' + wz'

 

b.) A minimal product-of-sums expression for F

(Group 0s) F(MPOS) =(y'+z')(w+x'+y+z')

 

6.) Use the map below to simplify the function:

F= S(0,2,3,7,8,10,11,13,15)

 

with the "don't care" conditions:

 

d= S(1,6,9)

soltest2-3.png

a.) Write all correct MSOP (mimimal sum-of-products) equations for the function above

 

F = x' + wz + yz

F = x' + wz + w'y

 

b.) Write all correct MSOP equations for the complement of the function above.

 

F ' = xz' + w'y'z

F ' = xz' + w'xy'

7.) (12 pts ) Determine the function implemented by each of the circuits below (in any correct form):

solmuxdec.png

 

soltest2-2b.png

 
8.) (10 pts) For the function shown in the 5 variable k-map above:

 

a.) Write an equation and draw an implementation of the this function using all NOR gates. The implementation should have the minimum possible propagation delay (you may use NORs with as many inputs as you like)

 

Start with MPOS form, and convert to NOR

 

b.) Write an expression for the function in And-Or-Invert (AOI) form

 

Group 0s, and invert

 

F(AOI) = (de' + bd + a'd'e + ab'd')'  

9.) Given the function F(x,y,z)= (x'+y)(y'+z')

 

For (a) , we will need to convert to CSOP form, for b we will need MSOP. 

 
Many possible ways: (1) Truth Table
						  (2) Distributive law
						  		(x'+y)(y'+z') = x'y' + yy' + x'z' + yz'
								then use k-map
						  (3) Realize this is MPOS of F, so
						  F'(MSOP) = xy' + yz
						  use this to get zeroes of map
Regardless of method, result is:
	F(MSOP) = x'y' + yz'

a.) (5 pts) Implement F using a multiplexer

p9.png

c.) (5 pts) Implement F using all NAND gates

p9c.png

10.) (8 Pts) Using the PAL below, implement the two functions F and G given as:

F(x,y,z) = S(0,2,3,7)

 

G(x,y,z) = P(0,2,3,4,6,7)

  For a PAL, we will need to convert to MSOP form, or F won't fit in the PAL. Using either algebra or K-maps, the reduced equations are:

 

F = x'z' + yz

 

G = y'z

 

Other answers that were reduced enough to fit in the PAL, though not minimum, were accepted as well

solpal.png

11.) (a.) (6 pts) Design a circuit which accepts as input any number between 0-5 (encoded in binary, of course). The output of the circuit will be the input number multiplied by two. Implement this circuit on the ROM shown below:

 

Truth table for problem as stated:
x y z   AB C D
0 0 0 0 0 0 0
0 0 1 0 0 1 0
0 1 0 0 1 0 0
0 1 1 0 1 1 0
1 0 0 1 0 0 0
1 0 1 1 0 1 0
1 1 0 X X X X
1 1 1 X X X X

rom.png















(b.) (Extra Credit - 3 points) Implement the boolean functions for the outputs in your truth table above with the minimum number of gates possible.



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On 5 Apr 2003, 16:57.