​Digital circuits Lab in latex

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Ortbivp_R_Yrneavat

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Digital circuits Lab ( full adder and multiplexer ) , - do the report in Latex -And convert anthor 2 reports to Latex

i did lab1 and lab 3 but i want you to convert to latex.

so do for lab 2 the same thing i send it to

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EEN210/ CSC303: Digital Circuits/ Digital Logic Design Lab Assignment 2 Full Adders and Multiplexers Prepared By: Eng. Marah Al Halabi Objectives • Study methods of generating circuits that perform arithmetic operations of full addition. • Get introduced to Logical Integrated Circuits (ICs). • Study an 8 to 1 Multiplexer in an experimental setup and verify its truth table. Required Equipment a) Training Board ETS 7000 b) K&H Digital Logic Boards c) Breadboard Cables d) Logic ICs e) Breadboard Figure 1: List of Equipment. Lab Experiment (i) (i)(a) Full Adder Exercise 1: Full Adder with Half Adders 1. Locate the digital circuit shown in Figure 2 on LT-04 K&H Digital Board and connect 3 switches to its input pins and two LEDs to its output pins, respectively. 2. For the Truth Table provided in Table 1, modify the state of the switches accordingly and notice the changes in the colour of the LED. Record the output in the form of 1’s and 0’s. 1 Figure 2: Full-Adder with Half-Adders. Table 1: Truth Table for Figure 2 X 0 0 0 0 1 1 1 1 Y 0 0 1 1 0 0 1 1 Ci 0 1 0 1 0 1 0 1 2 S Co • Question 1: Write the Boolean Expressions for the Sum and Carry Out given your truth table. .......................................................................................................................................................................... • Question 2: For Figure 2, draw two Karnaugh maps and discuss your results. ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... • Question 3: How does a full-adder differ from a half adder? Which one is more efficient in terms of calculations? .......................................................................................................................................................................... (i)(b) Exercise 2: Carry Out for Full-Adder 1. Locate the digital circuit shown in Figure 3 on LT-03 K&H Digital Board and connect 3 switches to its input pins and 1 LED to its output pin. Figure 3: Carry Out for Full-Adder. 2. Complete the Truth table for the Carry Out in Table 2. Table 2: Truth Table for Figure 3 X 0 0 0 0 1 1 1 1 Y 0 0 1 1 0 0 1 1 Ci 0 1 0 1 0 1 0 1 Co • Question 1: Write the simplified Boolean Expression for the Carry Out. .......................................................................................................................................................................... 3 • Question 2: Does Co for the Full-Adder give correct results? Explain the equivalence of this circuit to the Boolean Expression for the following expression: Co = XY Ci + XY Ci + XY Ci + XY Ci .......................................................................................................................................................................... Logical Integrated Circuits (ii) Introduction Logic gates like AND, NAND, OR, NOR and NOT perform their logical operations using electrical circuits. Logic gates consist of components like transistors, Diodes and resistors as shown in Figure 4. The way these components are connected together decides their logical function or behaviour (AND, OR and etc.). Figure 4: Inside a Logic Gate . The circuits are integrated together in one package or chip giving us our IC chip as shown in Figures 5 and 6. Figure 5: Integrated Circuit under X-RAY. Figure 6: Integrated Circuit in Real Life. IC chips come in two different packing methods, where the first one is called SIP (Single Inline Package Figure 7(a)),and the other is called DIP (Dual Inline package Figure 7(b)). For this lab we are going to use DIP ICs. Figure 7: Packing Methods. The method of placing an IC on a breadboard can be seen in Figure 8. Notice that you have to place the IC in the middle of the breadboard so that the pins don’t short each other. See also Figure 9 for your reference. The notch seen as 4 a semi circle denotes the top of the IC, where pin 1 is the first pin to the left of the notch. The ICs you will be dealing with in this lab have 16-pins each. To know the pin arrangement (pin number) for the IC, make the notch side of the IC face up, and look for a small circle. The pin next to that circle is Pin 1 and the pin on the opposite side of the circle is Pin 14. Figure 8: Placing an IC on a Breadboard. Figure 9: Breadboard Pins Surrounding the IC. (iii) 8-to-1 Multiplexer 74151 is an 8 lines-to-1 line multiplexer. It has the schematic representation shown in Figures 10 and 11. Selection lines C (MSB), B, and A (LSB) select the particular input to be multiplexed and applied to the output. Figure 10: 8 to 1 Multiplexer Schematic. 5 Figure 11: 8 to 1 Multiplexer Pin Diagram. Strobe G acts as an enable signal. If strobe = 1, the chip 74151 is disabled and output y = 0. If strobe = 0 then the chip 74151 is enabled and functions as a multiplexer. (iii)(a) Verify the Truth Table of an 8-to-1 Multiplexer 1. Construct the circuit shown in Figure 12 using Table 3. Make use of your ETS Trainer’s Power Module, Switches, and LEDs. Figure 12: Multiplexer Testing Circuit. Table 3: Multiplexer Inputs D0 0 D1 1 D2 0 D3 1 D4 0 2. Apply the inputs shown in Table 4. 6 D5 1 D6 0 D7 1 Table 4: Multiplexer Selection Lines/Outputs C 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 A 0 1 0 1 0 1 0 1 Y W 3. Write down your results. 4. Connect pin 7 to +5V and apply the same inputs in Table 3 and Table 4. 5. Observe the results and fill out the truth table. • Question 1: Based on your acquired results, what is the multiplexer doing in this circuit? Explain the functionality of multiplexer in general to back up your answer. .......................................................................................................................................................................... 7 EEN210: Lab Report 1 Logic Gates, Boolean Algebra, and Karnaugh Maps Aziz Ur Rehman 1032042 Waqas Bin Imran 1060931 Mohammed Alkaabi 1062283 Mohamed Jamal 1059415 Supervised By: Eng. Marah Al Halabi 1 Objectives • Get introduced to the basic logic integrated circuits. • Study the representation of the basic logic functions through truth tables. • Use Boolean Algebra to simplify logic equations. • Construct Digital Circuits from Boolean Expressions. • Build Karnaugh Maps for the generated truth tables. • Simplify Digital Circuits using Boolean Algebra and DeMorgan’s theorem. 2 Experimental Setup and Equipment Used Figure 1: List of Equipment. (a) Training Board ETS 7000: LEDs and power source (b) KH Digital Logic Board: Logic Gates board like AND, OR, XOR etc to implement and understand Boolean logic and solve problems. (c) Breadboard cables: Electrical conducting material used to connect circuit components. The specified LT K&H Digital Logic Board is placed into the designated area on the ETS7000 Trainer Board. It is then supplied with power by connecting the Digital Board with ”+5V” and ”GND” pins of the DC power Supply Module of the Trainer Board. Logic gates are used in real life to perform any Boolean functions, it executes the logic operation in which there are one or more inputs, yet it accommodates us simply a single output. In these experiments, we want to discover reality table of them by trials and afterward contrast out outcome and the regular truth table for each gate. 3 Procedure 3.1 Exercise ( a) This exercise required the output from the circuit shown in figure 2. 1. We connected inputs P, Q, R, and S to the 8 Bits Data Switches. 2. Pin Y9 is connected to any of the 8 Bits LED Displays. The output corresponds to the pin Y9. 3. we changed the values of the inputs and recorded the outputs based on the LED, by using the truth table provided in the Lab Manual. Figure 2: 2-Input AND-OR-INVERT Gate. 3.1 Exercise (b) Figure 3 shows the diagram of the gate logic circuit, it requires the use of an AND Gate and a NOT Gate. Figure 3: 2-Gate Logic Circuit. 1. We Connected the inputs C and D of the AND gate of the Digital Board with the 8 Bits Data Switches. 2. We connected the output Y2 of the AND gate to the input E of the NOT gate. 3. We took Output Y2 and Y3 from the Digital Board, and connected them to any 2 of the 8 Bits LED Displays. 4. We changed the inputs and recorded the outputs. 3.2 Exercise (a) By Given the following Boolean expression F = A + 𝐵̅ C, we utilized the basic logic gates on the LT-01 K&H Digital Board to construct its corresponding digital circuit. Figure 4 shows Gate Logic Circuit. Figure 4: Digital Logic Circuit. 1- We connected the input D of the AND gate to the input E of the NOT gate. 2- We connected the output Y2 of the AND gate to the input B of the OR gate. 3- We Connected the inputs A and B of the OR gate of the Digital Board with the 8 Bits Data Switches. 4- We Connected the input C of the AND gate of the Digital Board with the 8 Bits Data Switches. 5- We took Output Y1 of the OR gate from the Digital Board, and connected it to any one of the 8 Bits LED Displays. 6- We changed the inputs and recorded the outputs. 3.2 Exercise (b) The aim of this exercise is to simplify digital circuits using Boolean Algebra and DeMorgan's rule in order to construct the simplified circuit using the basic logic gates located on LT-01 K&H Board. In this exercise we Located the digital circuit shown in Figure 5 on LT-01 K&H Digital Board by simplified it to OR gate, AND gate and NOT gate as shown in figure 6 and connect 2 switches to its input pins. Then we Made the output connections to the LED's at the required points to complete the Truth table. We simplified the digital logic gate using DeMorgan's theorem to OR gate, AND gate and NOT gate as follows: A + 𝐴̅ B = A + B Figure 5: Digital Logic Circuit. Figure 6: Digital Logic Circuit. 1- We Connected the input T of the figure 2-16 of the Digital Board to the 8 Bits Data Switches. 2- We Connected the input U of the figure 2-16 of the Digital Board to the 8 Bits Data Switches. 3- We took Output Y10,Y11 and Y12 from the Digital Board, and connected them to any 3 of the 8 Bits LED Displays. 4- We changed the inputs and recorded the outputs. 3.2 Exercise (c) The aim of this exercise is to simplify digital circuits using Boolean Algebra and DeMorgan's rule in order to construct the simplified circuit using the basic logic gates located on LT-01 K&H Board. We traced the circuit outputs at different nodes. We simplified figure 7 using DeMorgan's theorem to OR gate and AND gate then we get as shown in figure 8. The expression is as follows: AC + BC = ( A + B ) C Figure 7: Digital Logic Circuit. Figure 8: Digital Logic Circuit. 1- We connected the output Y1 of the OR gate to the input C of the AND gate. 2- We Connected the inputs A and B of the OR gate of the Digital Board with the 8 Bits Data Switches. 3- We Connected the input C of the AND gate of the Digital Board with the 8 Bits Data Switches. 4- We took Output Y1 and Y3 from the Digital Board, and connected them to any 2 of the 8 Bits LED Displays. 5- We changed the inputs and recorded the outputs. 4 Results and Analysis 4.1 Exercise 1 (a) Figure 9 shows the experimental setup for this exercise. The 4-Input for NOR and AND Gates are highlighted. Figure 9: Experimental Setup for Exercise 1. Truth Table is: Question 1: Comparing rows 1, 2, and 3, why is the output Y unchanged despite changes in A and C? A and C remain 0 in the rows 1, 2, and 3. The outputs of the two AND Gates remain unchanged. As a result, the output from the NOR Gate remains the same. Question 2: Comparing rows 3 and 4, both have two 1 inputs. Why is Y different in line 4 compared to line 3? In row 3, the two 1 inputs are not for the same AND Gate. In row 4, the two 1 inputs (A and B) are for the same AND Gate. These changes depend on the input provided to the NOR Gate, hence changing the output Y. Question 3: Comparing rows 4, 5, and 6, why do additional 1 inputs in lines 5 and 6 have no effect on Y? When at least one AND Gate gives an output 1, The output Y becomes 0. The output of the first AND Gate is always 1 when A and B are 1 in all the 3 rows. Hence, even if give additional 1 inputs, Y remains unaffected. Question 4: Express the Boolean equation between the inputs and the outputs for Figure 2? DeMorgan's theorem is as follows: Y = ̅̅̅̅̅̅̅̅̅̅̅̅ 𝐴𝐵 + 𝐶𝐷 = ̅̅̅̅ 𝐴𝐵 . ̅̅̅̅ 𝐶𝐷 4.1 Exercise 1 (b) Figure 10 shows the experimental setup for this exercise. The 2-Input for AND and NOT Gates are highlighted. Figure 10: Experimental Setup for Exercise 1. Truth Table is: Question 1: What type of logic function will occur between A, B, and C for this circuit? AND function. Question 2: What type of logic function will occur between A, B, and D for this circuit? NAND function. 4.1 Exercise 2 (a) Figure 11 shows the experimental setup for this exercise. The 3-Input for AND,OR and NOT Gates are highlighted. Figure 11: Experimental Setup for Exercise 2. Truth Table is: 4.1 Exercise 2 (b) We simplified the complex system of Gates to use only 3 gates for its implementation, instead of the 4 highlighted in. Figure 12 shows the experimental setup for this exercise. The 3-Input for AND,OR and NOT Gates are highlighted. Figure 12: Experimental Setup for Exercise 2. Truth Table is: Question 1: What are the two inputs to Gate G1 in terms of A and B? A and 𝐴̅B Question 2: What is the output X in terms of A and B? A + 𝐴̅𝐵 Question 3: What is the output Y in terms of A and B? A+B Question 4: Based on your experimental results, what can we say (in Boolean terms) about the relationship between X and Y? (Express in terms of A and B.)? A + 𝐴̅𝐵 = A + B Question 5: For Figure 12, draw two Karnaugh maps and discuss your results for the inputs to G1 and G2? Since the Karnaugh Maps for both the outputs are the same, hence we can conclude that the expressions are the same, as well. 4.1 Exercise 2 (c) We simplified the complex system of Gates to use only 2 gates for its implementation, instead of the 6 highlighted in. Figure 13 shows the experimental setup for this exercise. The 3-Input for AND,OR and NOT Gates are highlighted. Figure 13: Experimental Setup for Exercise 2. Truth Table is: Question 1: In terms of variables A, B, and C, what are the values at U, V, W, X, and Y. Express the DeMorgan relationship between A, B, C, X, and Y. Next, complete the given truth table? U = AC V = BC W = A+B X = AC + BC = ( A + B ) C Y=(A+B)C Question 2: Draw the Karnaugh Maps for X and Y and discuss your results? Since the Karnaugh Maps for both the outputs are the same, hence we can conclude that the expressions are the same, as well. Question 3: Describe what does the simplified circuit for output X contain and construct it using the basic logic gates. Connect the switches to the inputs and LED to the output. Then fill out the truth table provided? It contain DeMorgan's theorem is X = ( A + B ) C . The simplified connection for this exercise just requires an AND and OR Gates. Question 4: Verify that your results for output X in the two tables are the same? The outputs are indeed the same. EEN210: Lab Report 3 Flip-Flops & Multisim Aziz Ur Rehman 1032042 Waqas Bin Imaran 1060931 Mohammed Alkaabi 1062283 Mohamed Jamal 1059415 Supervised By: Eng. Marah Al Halabi 1 Objectives • Study the characteristics • Get introduced to Multisim • Simulate digital logic circuits through Multisim 2 Experimental Setup and Equipment Used Figure 1: List of Equipment. (a) Training Board ETS 7000: LEDs and power source (b) KH Digital Logic Board: Logic Gates board like AND, OR, XOR etc to implement and understand Boolean logic and solve problems. (c) Breadboard cables: Electrical conducting material used to connect circuit components. (d) Multisim: Software used to simulate circuits The specified LT K&H Digital Logic Board is placed into the designated area on the ETS7000 Trainer Board. It is then supplied with power by connecting the Digital Board with ”+5V” and ”GND” pins of the DC power Supply Module of the Trainer Board. Logic gates are used in real life to perform any Boolean functions, it executes the logic operation in which there are one or more inputs, yet it accommodates us simply a single output. In these experiments, we want to discover reality table of them by trials and afterward contrast out outcome and the regular truth table for each gate. Procedure 3 3.1 Exercise (a) This exercise requires us to prove AND gate operation logic using Multisim 1. We open a blank schematic in Multisim. 2. We place down a 2-input AND gate, TTL supply, 2 switches, 100 ohm resistor, LED, logic converter and a digital ground. 3. We arrange the components on the schematic and wire them together to create the logic circuit. 4. We then execute the circuit and double click on logic converter to analyse the truth table. 3.2 Exercise (b) This exercise requires us to use Multisim to simulate circuits. Fig 2 shows the diagram for the logic circuit. 1. We open a blank schematic in Multisim 2. We place down 3 2-input NOR gates, 2 NOT gates, TTL supply, 2 switches and a digital ground. 3. We arrange the components on the schematic and wire them together to create the logic circuit. 4. We then execute the circuit and double click on logic converter to generate the truth table for the circuit Figure 2:Logic Circuit. 4 Results and Analysis 4.1 Exercise (a) Figure 3 shows the digital circuit we made to prove AND gate operation logic using multisim and the circuit’s truth table. Figure 3: Experimental Setup for Exercise 1. 4.1 Exercise (b) Figure 4 shows the digital circuit we made using multisim and the truth table for the circuit. . Question 1: Given the Truth Table and the Simplified Boolean Expression, what does this digital circuit operate as? XOR Question 2: Construct the circuit given the simplified Boolean Expression? 𝐴𝐵̅ + 𝐴̅𝐵 Question 3: Using NAND gates only, how will the circuit be constructed? Replace ever NOR and NOT gate with NAND
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