Question

1. If you were to design an air conditioning unit for your home, what electronics design elements would you incorporate (gates, input signals, output signals, feedback signals, etc.). Be as detailed as possible.

2. If you were an IC chip designer, what would be the steps to take to minimize the amount of gates used. Why is that important?

3. In one paragraph, why do you think learning about this branch of electronics, that is, digital electronics, is important?

   Problem 1. For following boolean expressions. 3 Points (1.5 point for each K and L):

   K = (AB)(A+B)C

   Hint: (A+B) = A B

   L = AB(C+D)

   Hint: (C+D) = C D and (AB) = A +B

4. Derive the gate schematic. Do not simplify either the expression nor the gate schematic.

5. Simplify the boolean expression using Boolean Algebra simplification

6. Derive the gate schematic after your simplification from b)

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   Problem 2: Complete the following table. Show your work. Remember, no credit will be given if no work is shown.

   1 Point (0.25 point each).

   Binary	Decimal
   	27
   10110101
   	999
   10101010

   
   

   
   

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

   Problem 3. From the schematic below,

8. What would the circuit look like, if only inverting gates (NAND or NOR gates) were used? 1 point.

9. Why would this be preferred, over using non-inverting gates? 1 point.

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    Problem 4: For the truth table shown below,

11. Obtain the circuit gate schematic. Simplify the schematic as much as possible. 1 Point.

12. Obtain the boolean expression. Simplify the expression as much as possible. 1 Point.

13. A	B	C	Output
    0	0	0	0
    0	0	1	1
    0	1	0	0
    0	1	1	1
    1	0	0	1
    1	0	1	1
    1	1	0	1
    1	1	1	1

    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

    Problem 5. For each of the following boolean equations. 3 Points (1 Point for each i, ii, and iii):

14. Construct the truth table.  

15. Can the expression get more simplified? If so, how?

16. i=xyz+xyz

    ii=x +xz+xyz

    iii=x y z+yz+z

    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

    Problem 6.

17. Draw out a NOR SR Latch by hand, showing S, R, Q, and Qbar signals. 1 Point.

18. Obtain the truth table of a NOR SR latch, showing all four modes on output Q. Those four modes include: Invalid, Hold, Set, and Reset. 1 Point.

19. If you were to connect LEDs to Q and Qbar, and set S to HIGH, as well as R to HIGH, which LED(s) would be on? 1 Point

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    Bonus. Up to 0.3 Points. Points will be added at the end of the semester after the final examination, and will benefit your final grade:

21. If you wish to do so, you may express any thoughts, considerations, concerns, or compliments you may have at this point.

22. What can be done, in order to improve this course for this and future semesters, if it is going to be offered virtually?

23. If you could change the world, would you change it, or would you change yours?

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Answer 1

Answer

Problem 1. For following boolean expressions. 3 Points (1.5 point for each K and L):
K = (AB)(A+B)C
Hint: (A+B) = A B
L = AB(C+D)
Hint: (C+D) = C D and (AB) = A +B

Derive the gate schematic. Do not simplify either the expression nor the gate schematic.Simplify the Boolean expression using Boolean Algebra simplification.Derive the gate schematic after your simplification from b)

K = (AB)(A+B)C	K = (AB)(A+B)C Hint: (A+B) = A B SUBSTITUTING A+B=AB K=AB.AB.C =ABC Simplified gate schematic
L=AB(C+D)	L = AB(C+D) Hint: (C+D) = C D and (AB) = A +B SUBSTITUTING (C+D) = C D and (AB) = A +B L=(A+B)CD

Problem 2: Complete the following table. Show your work. Remember, no credit will be given if no work is shown.1 Point (0.25 point each).

Decimal 00011011 10110101 1111100111 10101010

Decimal 27 181 999 170

Problem 3. From the schematic below, What would the circuit look like, if only inverting gates (NAND or NOR gates) were used? 1 point. Why would this be preferred, overusing non-inverting gates? 1 point.

NAND gate and NOR gate are universal gates,i.e. the combinations of universal gates can be used to get the basic operations. It can be used to form an inverter, an OR gate or an AND gate. The non-inverting gates like do not have this versatility since they can't produce an invert.

Problem 4: For the truth table shown below, Obtain the circuit gate schematic. Simplify the schematic as much as possible. 1 Point. Obtain the boolean expression. Simplify the expression as much as possible. 1 Point.

ABC	OUTPUT
000 001 010 011 100 101 110 111	0 1 0 1 1 1 1 1

K-map and final expression for the output in the truth table

Output =A+C

Problem 5. For each of the following boolean equations. 3 Points (1 Point for each i, ii, and iii):

Construct the truth table. Can the expression get more simplified? If so, how?

i=xyz+xyz
ii=x +xz+xyz
iii=x y z+yz+z

x	y	z	xyz	i	xz	xz+xyz	ii	yz	xyz+yz	iii
0	0	0	0	0	0	0	0	0	0	0
0	0	1	0	0	0	0	0	0	0	1
0	1	0	0	0	0	0	0	0	0	0
0	1	1	0	0	0	0	0	1	1	1
1	0	0	0	0	0	0	1	0	0	0
1	0	1	0	0	1	1	1	0	0	1
1	1	0	0	0	0	0	1	0	0	0
1	1	1	1	1	1	1	1	1	1	1

simplified expression i=xyz+xyz =xyz ii=x+xz+xyz=x(1+z)+xyz =x+xyz =x(1+yz) = x --1+x =1 iii = xyz + yz + z =z(yz +z+1 ) =z

Problem 6.

Draw out a NOR SR Latch by hand, showing S, R, Q, and Qbar signals. 1 Point.

Obtain the truth table of a NOR SR latch, showing all four modes on output Q. Those four modes include Invalid, Hold, Set, and Reset. 1 Point.

Truth table

S	R	Q	Q'	State
0	0	NC	NC	Hold
0	1	0	1	Latch RESET
1	0	1	0	Latch SET
1	1	X	X	Invalid

If you connect LEDs to Q and Qbar, and set S to HIGH, as well as R to HIGH, which LED(s) would be in an invalid state.