Objectives: Build and test Boolean functions, Truth tables, and Karnaugh Maps. Design some real world applications. Step1. Using Analyze Circuit option of the Logisim, design and test BCD-to-Seven-Segment Decoder using the following functions. Intuitively, 7-segment display must be used at the end of your circuit. If the 7-segment is appropriately linked with the automatically-generated circuit, the 7-segment will show you 0 to 9 numbers. Over 10 is out of mind this time. In order to make your 7-segment correctly work, it should be linked with each of output pins in the following order from the left-top pin of the 7-segment, clockwisely: gfab_cde.
The seven segment functions are:
Fa = ~a c + ~a b d + ~b ~c ~d + a ~b ~c
Fb = ~a ~b + ~a ~c ~d + ~a c d + a ~b ~c
Fc = ~a b + ~a d + ~b ~c ~d + a ~b ~c
Fd = ~a c ~d + ~a ~b c + ~b ~c ~d + a ~b ~c + ~a b ~c d
Fe = ~a c ~d + ~b ~c ~d
Ff = ~a b ~c + ~a ~c ~d + ~a b ~d + a ~b ~c
Fg = ~a c ~d + ~a ~b c + ~a b ~c + a ~b ~c
Note: Do not build your own circuits! The analyzer will generate the whole circuit for you except the 7-segment part.
Step2. Given the following truth table, generate Boolean expressions for each output followed by a circuit, step by step. Using Minimized tab of Analyze Circuit option, minimize your circuit and publish it as another circuit. From the second circuit you made in Step2, generate the other circuit using NAND gates only option. (Caution: As a result, you must have three circuits from Step2: the conventional circuit, the minimized circuit, and the circuit using only NAND gates.)
A B C T1 T2
0 0 0 1 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 0 1
1 0 1 0 1
1 1 0 0 1
1 1 1 0 1
Step3. Using Analyze Circuit option of the Logisim, enter the following expressions and build a circuit. After building the circuit, minimize the function and build it as another. And take a look at their Karnaugh maps and Truth tables using the Analyze Circuit option.
Step4. Assume a room has three doors and a switch by each door a single light in the room can be controlled.
Let x, y, and z denote the state of the switches
Assume the light is off if all switches are open(off)
Closing any switch turns the light on. Closing another switch will have to turn the light off.
Light is on if any one switch is closed and off if two (or no) switches are closed.
Light is on if all three switches are closed.
Develop a truth table. And then, build a logic circuit using the Analyze Circuit option. Simulate the circuit to check whether or not all the above conditions are satisfied.