11. Use NAND gates, NOR gates, or combinations of both to implement the following logic expressions as stated: (a) X = AB + CD + (A + B)(ACD + BE) (b) X = ABCD + DEF + AF (c) X = A[B + C(D + E)]
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Hello,
I don't know how to implement the expression for part(c).
I need to plot a scheme like answer2.PNG, but I have no idea how to start with.
Thanks.
![DDD
E
C
B
(c) X- A[B+ C(D+ E]]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5287cf77-5b14-4f79-830f-53ccb79ad7a9%2F6a2bd409-3fc3-491f-9bf1-8c06a28f7b9a%2Fsjsjet_processed.png&w=3840&q=75)
![11. Use NAND gates, NOR gates, or combinations of both to implement the following logic expressions as
stated:
(a) X = AB + CD + (A + B)(ACD + BE)
(b) X = ABCD + DEF + AF
(c) X = A[B + C(D + E)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5287cf77-5b14-4f79-830f-53ccb79ad7a9%2F6a2bd409-3fc3-491f-9bf1-8c06a28f7b9a%2F6s96075_processed.png&w=3840&q=75)
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- Discussion: 1. Simplify the following logical expression and implement them using suitable logic gates a = E2,4,6,10,14 b. F = I12,3,6 2 Determine whether or not the following equalities corect: a. A+B.C+Õ C = BC b. B(AO) +B C+ ACBOc) = AC 3. Convert the following expressions to SOP forms: A (A +B. C) -B b. (A + C)(Ã-B-Č+A.C-D) * 4. Write a Boolean expression for the following statement: Fisa "1" if A, B&C are all 1's or if only two of the variable is a"0". %3D * 5. Fing FDraw the AND and OR gate logic diagram of the expression. X=L[K(K+L)+M] Logic diagram using AND-OR gates Redraw the circuit using positive NOR gates. Logic diagram using positive NOR gates K(SW2) 0 0 0 0 1 1 1 1 INPUTS L (SW3) 00 1 1 0 0 1 1 M(SW4) 0 1 0 1 0 1 0 1Simplify the given Boolean expression and then draw a logic circuit using NOR Gates. X (A, B, C, D) = AB’C’ + AC + A’CD’
- Discussion: 1. Simplify the following logical expression and implement them using suitable logic gates. a F = E2,4,6,10,14 b. F I12,3,6 2 Determine whether or not the following equalities correct: a. A+B.C+ÕC = B C b. B(AO c) +BČ+ ACBOC) = AC 3. Convert the following expressions to SOP forms: a. (A +B.C) B b. (A + C)(à B Č+A C D) * 4. Write a Boolean expression for the following statement: Fisa "I" if A, B&C are all l's or if only two of the variable is a"0". 5. Find F %3D T IT DQuestions Q1) Why do NAND & NOR Gates called Universal Gates? Q2) Implement Ex-OR & Ex-NOR Gates using: a) NAND Gate only b) NOR Gate only Q3) Apply Demorgan's theorem and Boolean rules to simplify and draw the output of the following expression: Z= (AB(C+BD)+AB)CThe output X of a logic circuit depends on the input signals A, B and C as in the following logic expression: X = (A + B + C)C (а) Draw the logic diagram using only 2-input gates. Label each gate output. (b) Based on the label in (a), show the calculation for each gate outputs if i. A = 0, B = 0 and C = 0. ii. A = 0, B = 0 and C = 1. (c) Build a truth table for the following input signal combinations by including the output for each gates, according to the label in (a). A В C 1 1 1 1 1 1 1 1 1 1
- A circuit for adding two 3-bit 2's complement numbers (X2X1Xo and Y2Y1Y0) that uses Full Adder (FA) components is shown below. Write the full logic expression to detect overflow. Cout C3 X₂X₁ Xo FA Cir Cout C₂ Cout FA C S Z₂ Z₁ (Y₂) (Y₁ Yo Zo C₁ Cout FA CinLogic Gates:* 7404LS (NOT)* 7408LS (AND)* 7432LS (OR)* 7400LS (NAND)* 7402LS (NOR)* 7486LS (EX-OR)Or you can use 74HCxx versions. Task 2: 4 INPUT PRIORITY ENCODERa) Write the truth table.b) Find the outputs in terms of min terms using minimal expression.c) By using K map, find the simple/simplest expression of theoutputs.d) Draw the circuit diagram. (Simulation design will be accepted.)e) Simulate the circuit & explain your results. (Please do notdesign separate simulations for each output. You should design ONEsimulation including all inputs and outputs.)2- Experiment the boolean expression by using K-Map then draw by using logic gates ( NAND & NOR gates only) Y=A'B'C'D'+A'BC'D+ABCD+AB'CD+A' B'CD'+ABCD'+AB'CD'
- Consider F(A,B,C) = AB'C + B'C' + A'BC + A'C' 1. Determine how many logic gate inputs would be needed before any simplification. Do not count inputs to NOT gates 2. Use Boolean algebra rules to get the most simplified expression of F(A,B,C). Then determine how many logic gate inputs would be needed after simplification. Again, do not count inputs to NOT gates. 3. Expand the original expression into its canonical SOP representation. 4. Fill out the K-map below using the SOP canonical representation. Group the 1-cells according to the K-map simplification rules. Translate each group into its product term, OR these product terms together, and verify that the expression you get matches the one in Step 2. 5. Draw two circuits in CircuitVerse, one from the original expression for F(A,B,C), the other from the simplified expression in Step 2 or Step 4. Connect the inputs to both circuits, but separate their outputs. Verify through simulation that these two circuits are indeed equivalent. Take…1. a. i. Draw the gates required to build a half adder are ii. When simplified with Boolean Algebra (x + y)(x + z) simplifies to : iii. The output of a logic gate is 1 when all its inputs are at logic 0, the gate is either :1. Draw the gates required to build a half adder are 2. When simplified with Boolean Algebra (x + y)(x + z) simplifies to : 3. The output of a logic gate is 1 when all its inputs are at logic 0, the gate is either: 4. Simplify the Boolean expression AB+(AC)`+AB`C(AB+C) [6marks] 5. Use the Design Procedure to design a device that will change serial data to parallel data 6. Design 4 to 1 mutiplexer using the design procedure 7. Design 2 to 4 decoder 8. Design 4 bit comparator 9. Design 1 bit ALU 10. What is the difference between a combinational circuit and sequential circuit? Give example of each. 11. Describe the general setup for an arduino board when used to design a digital system. 12. Use K-Map to Minimize the following boolean function- F(A, B, C, D) = Σm(0, 1, 2, 5, 7, 8, 9, 10, 13, 15)