Lab Experience 5 Logic Circuits (A) Objectives Work with a logic circuit simulator to create and...

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Lab Experience 5 Logic Circuits (A) Objectives Work with a logic circuit simulator to create and test simple logic circuits Test the circuits by providing a full suite of inputs and checking that outputs are correct Give truth tables for circuits showing complete functionality of the circuits Background Figure 5.1 shows the various circuit components you will use in the exercises. Binary switch 2-input AND gate 3-input AND gate Do- D D' + NOT gate + 2-input OR gate Figure 5.1 The circuit components 3-input OR gate The small lines at the left of each gate are the connection points for input lines to the gate. Only one input line can be connected to each input connection point. The line attached to the right of the gate is the connection point for output lines from the gate. You may connect as many output lines to this point as you like. The number at the upper-right of a gate indicates the value of the output of the gate. In the case of the 2-input AND gate, this value would change to 1 if the two input lines to the gate have values of 1. Notice the 2 input AND ate This onto token three input The small lines at the left of each gate are the connection points for input lines to the gate. Only one input line can be connected to each input connection point. The line attached to the right of the gate is the connection point for output lines from the gate. You may connect as many output lines to this point as you like. The number at the upper-right of a gate indicates the value of the output of the gate. In the case of the 2-input AND gate, this value would change to 1 if the two input lines to the gate have values of 1. Notice the 3-input AND gate. This gate takes three input lines and produces an output of 1 only if all three inputs have values of 1. This gate could be replaced by two 2-input AND gates, but provides for simpler circuit diagrams. The binary switch provides a single output line with the current value of the switch. The value of the switch changes from 0 to 1 or 1 to 0 when we click on the switch. You should now run the lab software package and click the Logic Circuits button. This study source was downloaded by 100000865734375 from CourseHero.com on 06-19-2023 14:29:33 GMT-05:00 https://www.coursehero.com/file/73910045/Lab-5-Instructionspdf/ The example circuit In this exercise, you will work with a circuit that has already been constructed. To get started, select Open under the File menu and then choose the file example.cir. You should now see the circuit shown in Figure 5.2. Notice that both switches are originally in the 0 position. under the File menu and then choose the file example.cir. You should now see the circuit shown in Figure 5.2. Notice that both switches are originally in the 0 position. Logic Circuit EXAMPLE.CIR File Gates Changes Grid Da Figure 5.2 The example circuit The output value of the upper NOT gate is 1 since its input value from the upper switch is 0. The output value of the lower NOT gate is 1 since its input from the lower switch is 0. The input values to the AND gate are 0 from the upper switch and 1 from the lower NOT gate. Thus, the output value of the AND gate is 0. The inputs to the OR gate are 1 from the upper NOT gate and 0 from the AND gate. The output value of the OR gate is therefore 1. This would be considered the output for the circuit for this setting of the two switches. To set the values of the switches, select Set Switch from the Changes menu, as shown in Figure 5.3. Logic Circuit - EXAMPLE.CIR File Gates Changes Grid Connect Gates Set Switch Delete Figure 5.3 Preparing to set switches Now you can change or toggle the value on any switch by clicking on it. Exercise 5.1 Truth table for the example circuit Using A and B to denote the switches, on the Worksheet, fill in the truth table for the circuit by trying each setting of the switches and recording the output value of the circuit. Exercise 5.2 A slight change in the example circuit If you inadvertently made any changes to the example circuit, reload example.cir. Now we will experiment with changing the OR gate to an AND gate. First, it will help to keep track of where the gates are by locating them within a rectangular grid. To display the grid, select On from the Grid menu. Then choose Delete from the Changes menu. Now you can delete any gate or switch in your circuit by clicking on it. Click on the OR gate. The gate together with the lines coming into it should disappear. Next, select And Gate from the Gates menu. Click in the area previously occupied by the OR gate. You should see an AND gate appear in the grid cell where you clicked. Choose Connect Gates from the Changes menu. Now you can connect any gates and switches in the circuit, as long as connections between them are allowed. Here are some rules of thumb for connecting components: Name: Course: Worksheet Lab Experience 5 Logic Circuits (A) Exercise 5.1 Truth table for the example circuit A B Output Value 0 0 1 1 0 1 1 Exercise 5.2 A slight change in the example circuit Exercise 5.3 Another change A B Output Value 0 0 0 1 1 0 1 1 Exercise 5.3 Another change A B Output Value 0 0 0 1 1 0 1 1 Exercise 5.4 A simpler version of the example circuit Diagram of the simpler circuit: Exercise 5.5 A one-bit compare for equality circuit A B Output Value 0 0 0 1 1 0 1 1 Name: Course: Worksheet Lab Experience 5 Logic Circuits (B) Exercise 5.6 Sum-of-products for the example circuit Boolean expression for new version of the example circuit: Circuit diagram for the new version of the example circuit: Exercise 5.7 Two-input parity bit circuit 11 Exercise 5.7 Two-input parity bit circuit A B Odd Parity Bit 0 0 0 1 1 0 1 Boolean expression of two-input parity circuit: Circuit diagram for two-input parity circuit: Exercise 5.8 Three-input parity bit circuit A B C Odd Parity Bit 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Boolean expression of three-input parity circuit: Circuit diagram for three-input parity circuit: Exercise 5.9 Bits as operation codes A (code bit 1) B (code bit 2) C Result 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 Boolean expression: Circuit diagram: 3. Finish by selecting the desired receiver component. If that component has an available input connector, the computer will draw a new line between the two components. If no change occurs, select a different receiver component. In the current example, click on the NOT gate and then on the new AND gate. Now connect the lower AND gate to the new AND gate by first clicking on the lower AND gate and then clicking on the new AND gate. When you are finished editing the circuit, you can hide the grid by choosing On from the Grid menu. Fill in the truth table for the resulting circuit on the Worksheet by observing the output for each setting of the input switches. In case you might need this circuit later, you can save it, say as example2.cir, by taking the Save option under the File menu. Exercise 5.3 Another change Now, starting with the circuit which resulted from Exercise 5.2, change the original AND gate to an OR gate, and fill in the truth table for the resulting circuit. You might want to save this circuit as Example3.cir. Exercise 5.4 A simpler version of the example circuit There is a simpler circuit that will produce the same outputs as the demo circuit, the original Example.cir. Such a circuit can be made with a single 2-input AND gate and a single NOT gate. Choose New from the File menu and elect to delete the current circuit. The entire circuit should disappear. Display the grid. Choose Switch from the Gates menu, and place switches in the first and third cells of the leftmost column in the grid. Finally, drop an AND gate and a NOT gate into grid cells somewhere to the right of the switches, and hide the grid. Now experiment with various ways of connecting the components until you find a circuit giving the same truth table as the original example circuit. To try different ways of connecting the gates, you can delete lines and then reconnect the gates and switches. Draw the simpler circuit on the Worksheet. Exercise 5.5 A one-bit compare for equality circuit The one-bit compare for equality circuit outputs a 1 when both of its inputs are the same and a 0 otherwise. The design of this circuit is discussed in Section 4.4.3 of the text, and the resulting circuit is shown in Figure 5.4. Construct and test such a circuit with the simulator. Give the output values in the truth table on the Worksheet Logic Circuit File Gates Changes Grid Do Figure 5.4 One-bit equality circuit Logic Circuits (B) Objectives Practice giving circuit specifications using a truth table to show desired outputs for the various inputs Use the sum-of-products algorithm presented in Chapter 4 of the text to give Boolean expressions meeting the truth table specifications Use the lab software to construct and test the circuits corresponding to the Boolean expressions Understand how computer scientists can use tools of logic and mathematics to design some components of computer hardware Exercise 5.6 Sum-of-products for the example circuit Starting with the truth table of Exercise 5.1 of the lab manual and given below, apply the sum-of-products algorithm to obtain a Boolean expression for another circuit that would provide the same outputs as the example circuit. Then construct the new circuit with the simulator. Note how many more gates would be required for this circuit than appear in the original example circuit. After you have tested the circuit, give the Boolean expression and make a neat drawing of the circuit on the Worksheet. A B Output Value 0 0 1 0 1 1 1 0 1 1 Exercise 5.7 Two-input parity bit circuit Exercise 5.7 Two-input parity bit circuit An odd parity bit (see Exercise 20 of Chapter 4 of the text) is an extra bit, attached to the end of a string of bits, which is set to 1 or 0 in such a way that the entire string, including the parity bit, contains an odd number of 1's. For example, if the original string of bits is 01101010, then the parity bit should be a 1, yielding the result 011010101 with an odd number of 1's. If the original string is 100110, the parity bit is 0 8 This study source was downloaded by 100000865734375 from CourseHero.com on 06-19-2023 14:29:33 GMT-05:00 https://www.coursehero.com/file/73910045/Lab-5-Instructionspdf/ since the original string already has an odd number of 1's. In this exercise, design and test a circuit that produces as its output value the correct odd parity bit to accompany two one-bit input values. In other words, the original string has two bits, one bit for each input value. The final string will have three bits consisting of the two one-bit inputs and the one-bit output from the circuit. Thus the output value should be 1 in the case where both inputs are 0 and in the case where both inputs are 1. Fill in the truth table on the Worksheet, apply the sum-of-products algorithm to derive the Boolean expression, construct the circuit, and finally test it. Give the Boolean expression and a neat drawing of the circuit on the Worksheet. Exercise 5.8 Three-input parity bit circuit me case where both inputs are 1. Fill in the truth table on the Worksheet, apply the sum-of-products algorithm to derive the Boolean expression, construct the circuit, and finally test it. Give the Boolean expression and a neat drawing of the circuit on the Worksheet. Exercise 5.8 Three-input parity bit circuit Following the design technique of the first two exercises, construct and test a three-bit parity circuit. Exercise 5.9 Bits as operation codes Later in the course, you will study in some depth how certain bits in computer instructions are used as codes to let the computer know which operation to perform. For example, one code might indicate that an addition should be performed, while another code might indicate that a compare for equality should be performed. In this exercise, you will design, construct, and test a circuit that performs this kind of function. Your circuit will have three inputs and a single output. The first two inputs are used as codes to indicate what should be done to the third input to produce the output. There are four possibilities for the two-bit codes, 00, 01, 10, and 11. We'll use the codes as follows: (1) (2) (3) (4) If the first two input values are 0 (code 00), the output should be 0, no matter what the third input is. Here the function of the circuit becomes a set-to-zero function on the third input. If the first input is 0 and the second is 1 (code 01), the output should be the same as the third input. The function of the circuit is the identity function on the third input. If the first input is 1 and the second is 0 (code 10), the output should be the negation of the third input. If the first two inputs are 1 (code 11), the output should be 1 no matter what the third input is. The function is a set-to-one operation. Make a truth table that gives the appropriate output values according to this discussion, write the corresponding Boolean expression, construct the circuit with the simulator, and test the circuit by checking the output values for each setting of the switches. Lab Experience 5 Logic Circuits (A) Objectives Work with a logic circuit simulator to create and test simple logic circuits Test the circuits by providing a full suite of inputs and checking that outputs are correct Give truth tables for circuits showing complete functionality of the circuits Background Figure 5.1 shows the various circuit components you will use in the exercises. Binary switch 2-input AND gate 3-input AND gate Do- D D' + NOT gate + 2-input OR gate Figure 5.1 The circuit components 3-input OR gate The small lines at the left of each gate are the connection points for input lines to the gate. Only one input line can be connected to each input connection point. The line attached to the right of the gate is the connection point for output lines from the gate. You may connect as many output lines to this point as you like. The number at the upper-right of a gate indicates the value of the output of the gate. In the case of the 2-input AND gate, this value would change to 1 if the two input lines to the gate have values of 1. Notice the 2 input AND ate This onto token three input The small lines at the left of each gate are the connection points for input lines to the gate. Only one input line can be connected to each input connection point. The line attached to the right of the gate is the connection point for output lines from the gate. You may connect as many output lines to this point as you like. The number at the upper-right of a gate indicates the value of the output of the gate. In the case of the 2-input AND gate, this value would change to 1 if the two input lines to the gate have values of 1. Notice the 3-input AND gate. This gate takes three input lines and produces an output of 1 only if all three inputs have values of 1. This gate could be replaced by two 2-input AND gates, but provides for simpler circuit diagrams. The binary switch provides a single output line with the current value of the switch. The value of the switch changes from 0 to 1 or 1 to 0 when we click on the switch. You should now run the lab software package and click the Logic Circuits button. This study source was downloaded by 100000865734375 from CourseHero.com on 06-19-2023 14:29:33 GMT-05:00 https://www.coursehero.com/file/73910045/Lab-5-Instructionspdf/ The example circuit In this exercise, you will work with a circuit that has already been constructed. To get started, select Open under the File menu and then choose the file example.cir. You should now see the circuit shown in Figure 5.2. Notice that both switches are originally in the 0 position. under the File menu and then choose the file example.cir. You should now see the circuit shown in Figure 5.2. Notice that both switches are originally in the 0 position. Logic Circuit EXAMPLE.CIR File Gates Changes Grid Da Figure 5.2 The example circuit The output value of the upper NOT gate is 1 since its input value from the upper switch is 0. The output value of the lower NOT gate is 1 since its input from the lower switch is 0. The input values to the AND gate are 0 from the upper switch and 1 from the lower NOT gate. Thus, the output value of the AND gate is 0. The inputs to the OR gate are 1 from the upper NOT gate and 0 from the AND gate. The output value of the OR gate is therefore 1. This would be considered the output for the circuit for this setting of the two switches. To set the values of the switches, select Set Switch from the Changes menu, as shown in Figure 5.3. Logic Circuit - EXAMPLE.CIR File Gates Changes Grid Connect Gates Set Switch Delete Figure 5.3 Preparing to set switches Now you can change or toggle the value on any switch by clicking on it. Exercise 5.1 Truth table for the example circuit Using A and B to denote the switches, on the Worksheet, fill in the truth table for the circuit by trying each setting of the switches and recording the output value of the circuit. Exercise 5.2 A slight change in the example circuit If you inadvertently made any changes to the example circuit, reload example.cir. Now we will experiment with changing the OR gate to an AND gate. First, it will help to keep track of where the gates are by locating them within a rectangular grid. To display the grid, select On from the Grid menu. Then choose Delete from the Changes menu. Now you can delete any gate or switch in your circuit by clicking on it. Click on the OR gate. The gate together with the lines coming into it should disappear. Next, select And Gate from the Gates menu. Click in the area previously occupied by the OR gate. You should see an AND gate appear in the grid cell where you clicked. Choose Connect Gates from the Changes menu. Now you can connect any gates and switches in the circuit, as long as connections between them are allowed. Here are some rules of thumb for connecting components: Name: Course: Worksheet Lab Experience 5 Logic Circuits (A) Exercise 5.1 Truth table for the example circuit A B Output Value 0 0 1 1 0 1 1 Exercise 5.2 A slight change in the example circuit Exercise 5.3 Another change A B Output Value 0 0 0 1 1 0 1 1 Exercise 5.3 Another change A B Output Value 0 0 0 1 1 0 1 1 Exercise 5.4 A simpler version of the example circuit Diagram of the simpler circuit: Exercise 5.5 A one-bit compare for equality circuit A B Output Value 0 0 0 1 1 0 1 1 Name: Course: Worksheet Lab Experience 5 Logic Circuits (B) Exercise 5.6 Sum-of-products for the example circuit Boolean expression for new version of the example circuit: Circuit diagram for the new version of the example circuit: Exercise 5.7 Two-input parity bit circuit 11 Exercise 5.7 Two-input parity bit circuit A B Odd Parity Bit 0 0 0 1 1 0 1 Boolean expression of two-input parity circuit: Circuit diagram for two-input parity circuit: Exercise 5.8 Three-input parity bit circuit A B C Odd Parity Bit 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Boolean expression of three-input parity circuit: Circuit diagram for three-input parity circuit: Exercise 5.9 Bits as operation codes A (code bit 1) B (code bit 2) C Result 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 Boolean expression: Circuit diagram: 3. Finish by selecting the desired receiver component. If that component has an available input connector, the computer will draw a new line between the two components. If no change occurs, select a different receiver component. In the current example, click on the NOT gate and then on the new AND gate. Now connect the lower AND gate to the new AND gate by first clicking on the lower AND gate and then clicking on the new AND gate. When you are finished editing the circuit, you can hide the grid by choosing On from the Grid menu. Fill in the truth table for the resulting circuit on the Worksheet by observing the output for each setting of the input switches. In case you might need this circuit later, you can save it, say as example2.cir, by taking the Save option under the File menu. Exercise 5.3 Another change Now, starting with the circuit which resulted from Exercise 5.2, change the original AND gate to an OR gate, and fill in the truth table for the resulting circuit. You might want to save this circuit as Example3.cir. Exercise 5.4 A simpler version of the example circuit There is a simpler circuit that will produce the same outputs as the demo circuit, the original Example.cir. Such a circuit can be made with a single 2-input AND gate and a single NOT gate. Choose New from the File menu and elect to delete the current circuit. The entire circuit should disappear. Display the grid. Choose Switch from the Gates menu, and place switches in the first and third cells of the leftmost column in the grid. Finally, drop an AND gate and a NOT gate into grid cells somewhere to the right of the switches, and hide the grid. Now experiment with various ways of connecting the components until you find a circuit giving the same truth table as the original example circuit. To try different ways of connecting the gates, you can delete lines and then reconnect the gates and switches. Draw the simpler circuit on the Worksheet. Exercise 5.5 A one-bit compare for equality circuit The one-bit compare for equality circuit outputs a 1 when both of its inputs are the same and a 0 otherwise. The design of this circuit is discussed in Section 4.4.3 of the text, and the resulting circuit is shown in Figure 5.4. Construct and test such a circuit with the simulator. Give the output values in the truth table on the Worksheet Logic Circuit File Gates Changes Grid Do Figure 5.4 One-bit equality circuit Logic Circuits (B) Objectives Practice giving circuit specifications using a truth table to show desired outputs for the various inputs Use the sum-of-products algorithm presented in Chapter 4 of the text to give Boolean expressions meeting the truth table specifications Use the lab software to construct and test the circuits corresponding to the Boolean expressions Understand how computer scientists can use tools of logic and mathematics to design some components of computer hardware Exercise 5.6 Sum-of-products for the example circuit Starting with the truth table of Exercise 5.1 of the lab manual and given below, apply the sum-of-products algorithm to obtain a Boolean expression for another circuit that would provide the same outputs as the example circuit. Then construct the new circuit with the simulator. Note how many more gates would be required for this circuit than appear in the original example circuit. After you have tested the circuit, give the Boolean expression and make a neat drawing of the circuit on the Worksheet. A B Output Value 0 0 1 0 1 1 1 0 1 1 Exercise 5.7 Two-input parity bit circuit Exercise 5.7 Two-input parity bit circuit An odd parity bit (see Exercise 20 of Chapter 4 of the text) is an extra bit, attached to the end of a string of bits, which is set to 1 or 0 in such a way that the entire string, including the parity bit, contains an odd number of 1's. For example, if the original string of bits is 01101010, then the parity bit should be a 1, yielding the result 011010101 with an odd number of 1's. If the original string is 100110, the parity bit is 0 8 This study source was downloaded by 100000865734375 from CourseHero.com on 06-19-2023 14:29:33 GMT-05:00 https://www.coursehero.com/file/73910045/Lab-5-Instructionspdf/ since the original string already has an odd number of 1's. In this exercise, design and test a circuit that produces as its output value the correct odd parity bit to accompany two one-bit input values. In other words, the original string has two bits, one bit for each input value. The final string will have three bits consisting of the two one-bit inputs and the one-bit output from the circuit. Thus the output value should be 1 in the case where both inputs are 0 and in the case where both inputs are 1. Fill in the truth table on the Worksheet, apply the sum-of-products algorithm to derive the Boolean expression, construct the circuit, and finally test it. Give the Boolean expression and a neat drawing of the circuit on the Worksheet. Exercise 5.8 Three-input parity bit circuit me case where both inputs are 1. Fill in the truth table on the Worksheet, apply the sum-of-products algorithm to derive the Boolean expression, construct the circuit, and finally test it. Give the Boolean expression and a neat drawing of the circuit on the Worksheet. Exercise 5.8 Three-input parity bit circuit Following the design technique of the first two exercises, construct and test a three-bit parity circuit. Exercise 5.9 Bits as operation codes Later in the course, you will study in some depth how certain bits in computer instructions are used as codes to let the computer know which operation to perform. For example, one code might indicate that an addition should be performed, while another code might indicate that a compare for equality should be performed. In this exercise, you will design, construct, and test a circuit that performs this kind of function. Your circuit will have three inputs and a single output. The first two inputs are used as codes to indicate what should be done to the third input to produce the output. There are four possibilities for the two-bit codes, 00, 01, 10, and 11. We'll use the codes as follows: (1) (2) (3) (4) If the first two input values are 0 (code 00), the output should be 0, no matter what the third input is. Here the function of the circuit becomes a set-to-zero function on the third input. If the first input is 0 and the second is 1 (code 01), the output should be the same as the third input. The function of the circuit is the identity function on the third input. If the first input is 1 and the second is 0 (code 10), the output should be the negation of the third input. If the first two inputs are 1 (code 11), the output should be 1 no matter what the third input is. The function is a set-to-one operation. Make a truth table that gives the appropriate output values according to this discussion, write the corresponding Boolean expression, construct the circuit with the simulator, and test the circuit by checking the output values for each setting of the switches.