LOGIC DESIGN AND SWITCHING THEORY
LAB#3
Digital logic circuits analysis and converting Boolean expressions to
digital circuits
OBJECTIVES
1. To learn how to directly convert a Boolean expression to circuit.
2. To learn how to analyze a given digital logic circuit by finding the Boolean expression
that represents the circuit
3. To learn how to analyze a given digital logic circuit by finding the truth table that
represents the circuit.
Example:
Z = A + B.C’
The above function is implemented in the following digital logic Circuit
Now after drawing the circuit above using EWB we find that its truth table is as shown below
( notice that logic 1 means connect the input to the Vcc line, and logic 0 means connecting the
input to the ground)
A B C Z
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
Logic Design & Switching Theory 1
LOGIC DESIGN AND SWITCHING THEORY
Lab Tasks
Task 1: Converting Boolean expressions into circuits
Convert the following Boolean expression to a circuit, draw the circuit on EWB and simulate it
to fill-in its truth table shown below.
X = Y + Z . Y’
Draw the circuit in the space below
Now, fill-in the truth table of the circuit you drawn
Y Z X
0 0 0
Logic Design & Switching Theory 2
LOGIC DESIGN AND SWITCHING THEORY
0 1 1
1 0 11
1 1 1
Task 2: Converting Boolean expressions into circuits
Convert the following Boolean expression to a circuit, draw the circuit on EWB and simulate it
to fill-in its truth table shown below.
D = ( A . B ) + ( C’ . A )
A B C D
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
.
1 0 1 0
1 1 0 1
1 1 1 1
Logic Design & Switching Theory 3
LOGIC DESIGN AND SWITCHING THEORY
Logic Design & Switching Theory 4
LOGIC DESIGN AND SWITCHING THEORY
Task 3: Digital logic circuit analysis – Finding the Boolean expression of a given circuit
Find the Boolean expression of the following circuit, draw the circuit on EWB and simulate it to
fill-in its truth table shown below.
Note: the logic converter tool from EWB to fill-in the following table. For that, you need to
connect the A, B and C inputs of the logic converter to X, Y and Z lines, respectively. Further,
you need to connect the ‘out’ line of the logic converter to W. As shown in the following
diagram
-----------------
W =(X’.Y)(Y+Z)
Logic Design & Switching Theory 5
LOGIC DESIGN AND SWITCHING THEORY
X Y Z W
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
Task 4: Digital logic circuit analysis – Finding the Boolean expression of a given circuit
Find the Boolean expression of the following circuit,
D= A.B’(A+C)
Draw the circuit on EWB and simulate it to fill-in its truth table shown below (use logic
converter please).
Logic Design & Switching Theory 6
LOGIC DESIGN AND SWITCHING THEORY
A B C D
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 0
Task 5: Logic circuits with multiple outputs
Find the Boolean expression of the outputs of the following circuit,
-----------
D= (A+B’+C)
E= (A+B’+C)
Logic Design & Switching Theory 7
LOGIC DESIGN AND SWITCHING THEORY
Draw the circuit on EWB and simulate it to fill-in its truth table shown below (use logic
converter please).
Note: You need to use the logic converter two times, once for the output D, and another time for
the second output E.
A B C D E
0 0 0 0 1
0 0 1 0 10
0 1 0 0 0
0 1 1 0 11
1 0 0 0 1
1 0 1 0 11
1 1 0 0 1
1 1 1 0
0 1
Task 6: Finding the Boolean expression of a given circuit using the logic converter
Logic Design & Switching Theory 8
LOGIC DESIGN AND SWITCHING THEORY
Draw the following circuit on EWB and then find its Boolean expression using the logic
converter.
F=C’D’E+BC+A
Logic Design & Switching Theory 9
LOGIC DESIGN AND SWITCHING THEORY
Task 7: Converting Boolean expressions to circuits using the logic converter
Use the logic converter to realize the following circuit using suitable logic gates:
AB'C (BD + CDE) + AC'
Logic Design & Switching Theory 10
