1.
We will
be analyzing the transistor circuit given below for all possible inputs of A
and B. Both circuit diagrams are identical. I have provided two copies for you
to write on if you choose to print it.
a) For all inputs A and B
indicate in the table below whether each transistor (labeled 1-6) conducts
(i.e., act like a piece of wire, denoted “1”) or does not conduct (i.e.,
acts like an open circuit, denoted “0”).
Finally, indicate the value (0 or 1) of the output Z.
A
B
1
2
3
4
5
6
Z
0
0
0
1
1
0
1
1
b) Give a logical expression
that describes Z in terms of A and B. You can base your
answer on the circuit instead of the truth table.
Simulation:
2. Truth table for a half-adder is given in
Table 1. Design a half-adder circuit on Logisim that has two inputs, A and B
and produces the expected output for Sum and Carry out. You can use sum of
products (SOP) to come up with your mathematical representation.
In your design, employ logic gates, such as AND, NOT, XOR and OR.
Table 1.
Half-adder truth table
A
B
Carry
out
Sum
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
Click on Project -> Analyze Circuit. Is
the truth table correct? If not, fix your circuit.
If so, what is the minimal sum of products (SOP) expression given for Sum under
the Minimized tab?
Click on Build Circuit and select the option
to use NAND gates only. When you are submitting your Lab report, show your
circuit (take a screenshot and paste it here) or draw the resulting simplified
circuit in NAND gates. Save the result.
3. Consider the truth table given below.
Calculate a logical expression that describes Z in terms of A and
B and C.
A
B
C
Z
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
Implement your design in
Logisim. Click on
Project -> Analyze Circuit. Is the truth table correct? If not, fix your
circuit. If so, what is the minimal sum of products (SOP) expression given?
Click on Build Circuit and select the option
to use NAND gates only. Save the result. When you are submitting your Lab, show
your circuit. Do NOT draw this circuit.
