. Given the function: F(a, b, c) = (a + b)’c + a b c’ + a c a) Create the truth table for function F. b) Implement F by means of an 8-to-1 Multiplexer using block diagrams. c) Implement F by means of a 3-to-8 Decoder using block diagrams and any gates if needed.
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A: The solution can be achieved as follows.
a) Create the truth table for function F.
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- 3- A-) Implement the Boolean function (F) with a 4 X1 multiplexer and two-input-NOR gates. Connect inputs A and B to the selection lines. The input requirement for the four data lines will be a function of variables C and D. These values are obtained by expressing F as a function of C and D for each of the four cases when AB = 00, 01 ,10 and 11. B-) Implement the Boolean function with a 8 X 1 multiplexer. Connect inputs A,B and C to selection lines. F(A, B, С, D) - 2 (1, 3, 5, 9, 10, 14, 15) А So В S1 4 x 1 MUX 1 Y F 2 3Design an 8-to-1 multiplexer using 4-to-1 and 2-to-1 multiplexers only. you will need to provide truth table, logic expression and circuit diagram.Create a circuit to generate odd parity bit for a 3-bit code. a. Construct the truth table. b. Use K-map to simplify the circuit. c. Draw the circuit with minimum number of gates. (I did the question myself, but I'm confused as to why the K-map does not provide the simplified circuit to build the minimum number of gates)
- Task 6: Simplifying Boolean functions in EWB using the logic converter Simplify the following Boolean expression in EWB using the logic converter F (A, B, C) = AB'C'+ A'B'C'+ A'BC'+ A'B'CLogic 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.)4. Use the Word table tool to construct the truth table for this circuit. Be sure to include intermediate values. Insert column headings in the first row. Be sure to use the Insert > Equation tool so that standard Boolean logic symbols are displayed in the headings. A B. D In the circuit implementation of an 8-bit adder, explain why the carry bit connection of the least- significant bit is connected to ground. Explain in words what values for A, B, C, D, E will cause a 1 to appear at point X. A B E
- 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…Y 3. 4 Fill in the blanks in the truth table of the given digital circuit. Use ' for NOT gate e.g X'. Use paranthesis for combining two logic gates e.g Z.(X+Y) or (Y+Z).(X+Y)*A traffic light system uses logic gates as part of the control system. The system is operated when the output D has the value . This happens when either (a) signal A is red or (b) signal B is green and signals B and C are both red( NOTE: Assume for this problem that red=0 and green =1) Deduce the truth table for the system and the Boolean expression from the truth table, Hence Design a logic circuit or network
- Solve the problem and simplify the output function using Quine–Mc Cluskey Methods. The following requirements must be met in solving the problem. Requirement:a. Truth Tableb. Timing Diagramc. Quine – Mc Cluskey Method d. Logic Diagram A private company wants to decide on a certain issue. Each of the four officials has an equal share of voting right. At least two of them must approve the solution in order to implement it. Each of them has a switch which closes to vote YES and open to vote NO.DISCUSSION: 1- Is the Gray code arithmetic code? Why? Where this code usėd? 2- What is the parity bit? 13- Design five - bit odd parity checker? 4- a) What are the main applications of the comparator? /b) Design two – two bit comparator. -5- Convert five.bit Gray to binary code, write truth table and draw the circuit diagram. 2-5Draw the AND and OR gate logic diagram of the expression. X=[[K(K+L) +M] Logic diagram using AND-OR gates Redraw the circuit using positive NOR gates. Logic diagram using positive NOR gates