Exercise #2: Basic Logic Circuits and Functions
Revision: September 7, 2004
I am submitting my own work, and I am aware of the penalties for
cheating that may be assessed if I submit work that is not my own.
___________________________
Sign Name
Print Name: Dan Strother
ID#:
_____________
Date
Section:
For lab assistant use: I observed the student designing, implementing, and demonstrating the circuits and/or other work
for this lab, or the student demonstrated adequate knowledge of their submitted work (otherwise, circle “no demo” and
deduct points as appropriate).
This lab was (circle one)
ON TIME
circle if
LATE (-20%)
Lab assistant signature
Problem 1.
A
0
0
1
1
Date
Time
(7 points) Complete the truth tables below.
B
0
1
0
1
F
1
0
0
0
A
0
0
1
1
NOR
A
0
0
0
0
1
1
1
1
Overall score (do not deduct late points):
NO DEMO
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
B
0
1
0
1
F
0
0
0
1
A
0
0
1
1
B
0
1
0
1
AND
F
0
1
1
1
0
0
1
1
F=A’C + B
Exercise #2 Submission Form
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
F
1
0
0
1
A
0
1
F
1
0
INV
EQV
F
0
0
1
0
0
1
1
0
F=AB’C + BC’
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
F
0
1
1
0
0
1
1
0
F=BC’ + B’C
7 pages
Lab #2: Basic Logic Circuits and Functions
Problem 2.
Page 2
(8 points) Complete the truth tables for the circuit in Figure 1, using LLV and LHV in
the physical truth table and “1’s and 0’s” in the logical truth table.
SW1
LLV
LLV
LHV
LHV
SW2
LLV
LHV
LLV
LHV
F
LHV
LHV
LHV
LLV
Physical truth table
SW1
0
0
1
1
SW2
0
1
0
1
F
1
1
1
0
G (= F’)
0
0
0
1
Logical truth table
Describe in your own words how the circuit of figure 1 can be interpreted as implementing
an AND relationship:
When both SW1 AND SW2 are closed, the output is low.
Describe in your own words how the circuit of figure 1 can be interpreted as implementing
an OR relationship:
When either SW1 OR SW2 is open, the output is high.
Problem 3.
(6 points) Complete the truth tables for the circuit in Figure 2, using LLV and LHV in
the physical truth table and “1’s (for LHV) and 0’s” in the logical truth table (2 points).
SW1
LLV
LLV
LHV
LHV
SW2
LLV
LHV
LLV
LHV
F
LLV
LHV
LHV
LHV
Physical truth table
SW1
0
0
1
1
SW2
0
1
0
1
F
0
1
1
1
G (= F’)
1
0
0
0
Logical truth table
Which column (F or G or both) can show the AND relationship? _both_
Complete the following sentence: The circuit in figure 2 demonstrates the OR relationship by
driving the output F to _LHV_ when the SW1 is _closed_ or SW2 is _closed_; and the AND
relationship by driving the output F to _LLV_ when SW1 is _open_ and SW2 is _open_.
Sketch a circuit below using parallel switches and a single resistor that drives an output F to
LLV if SW1 or SW2 are at LHV (assume LHV closes the switch). This amounts to
rearranging the circuit configuration in figure 2.
Lab #2: Basic Logic Circuits and Functions
Page 3
(4 points) Based on these exercises, state a simple theorem for “converting”
between an AND interpretation and an OR interpretation of a given circuit.
You can convert between AND and OR interpretations by inverting both the inputs
and outputs simultaneously.
Problem 4.
Problem 5:
(6 points) Sketch a circuit using just
switches and resistors that can drive
an output F to LLV if two signals A
or B are at LHV, and if a third signal
C is at LHV regardless of the state of
A and B. Then, state an alternate
interpretation of the circuit sketched
in problem 5.
Alternate interpretation (Switch assertion levels, i.e. use “LLV” instead of “LHV” and vice-versa):
(10 points) Complete the voltage truth tables below (enter “on” or “off” under each
transistor entry), and enter the gate name and schematic shapes in the tables.
Problem 6:
Vdd
A
Q1
Q2
B
F
Q3
A
B
Q1 Q2 Q3 Q4
L
L
H
H
L
H
L
H
on
on
off
off
A
B
Q1 Q2 Q3 Q4
F
L
L
H
H
L
H
L
H
on
on
off off
on
on
off
off
off
on
off
off on off
on off off
on on off
on
off
on
off
F
off off on
on off on
off on on
on on off
Gate
Name
NAND
AND shape
OR shape
Q4
Vdd
A
Q1
B
Q2
F
Q3
Q4
Gate
Name
NOR
AND shape
OR shape
Lab #2: Basic Logic Circuits and Functions
Page 4
Vdd
A
Q1
Q5
B
F
Q2
Q6
Q3
Q4
Gate
Name
A
B
Q1 Q2 Q3 Q4
L
L
H
H
L
H
L
H
on
on
off
off
A
B
Q1 Q2 Q3 Q4
L
L
H
H
L
H
L
H
on
on
off
off
A
B
C
Q1 Q2 Q3 Q4 Q5 Q6
F
L
L
L
on
on
on
off
off
off
on
L
L
L
H
H
H
H
L
H
H
L
L
H
H
H
L
H
L
H
L
H
on
on
on
off
off
off
off
on
off
off
on
on
off
off
off
on
off
on
off
on
off
off
on
on
off
off
on
on
off
off
off
on
on
on
on
on
off
on
off
on
off
on
off
on
off
on
off
off
off
on
off
on
off
F
off off off
off on on
on off on
on on on
OR
AND shape
OR shape
Vdd
A
Q1
Q2
Q5
B
F
Q3
Q6
Q4
on
off
on
off
Gate
Name
F
off off off
on off off
off on off
on on on
AND
AND shape
OR shape
Vdd
A
Q1
Q2
B
C
Q3
F
Q4
Q6
Q5
Enter the logic equation for the 3-input circuit above:
Problem 7.
F = C’(A’+B’)
(6 points) Sketch circuits for the following logic equations (a ‘ following a variable
means the variable should be inverted). Minimization of the circuit is not required.
F = A’.B.C + A’.B’.C’ + A’.B’
Lab #2: Basic Logic Circuits and Functions
Page 5
F = (A’.B’) + (A’ + B’ + C)’
F = (A’ + C)’ . ((A’ + C) . B’)’
Problem 8.
(8 points) Write logic equations for the following circuits. Minimization is not
required.
A
A
B
B
F
F
C
C
D
F = (AB’) + (BC)
F = (AB’) + (CD)
A
B
F
A
B
C
C
F
D
D
F = (A + C)’(C’ + D)
F = (AB’C) + (B’D) + (AD)
Lab #2: Basic Logic Circuits and Functions
Problem 9:
Page 6
(10 points) Write the Boolean equation that defines the temperature controller problem,
and the sketch the circuit:
F = S(A + B)
Problem 10: (15 points) Build the temperature controller circuit on
Digilab’s breadboard, and then test the circuit. Complete
the truth table as you proceed through the test. Have a
lab assistant inspect your circuit.
A
L
L
L
L
H
H
H
H
B
L
L
H
H
L
L
H
H
C
L
H
L
H
L
H
L
H
F
Problem 11: (20 points) Build and test the light switch circuit. Complete
the truth table as you proceed through the test. Write the
Boolean equation and sketch the circuit.
A
L
L
L
L
H
H
H
H
B
L
L
H
H
L
L
H
H
C
L
H
L
H
L
H
L
H
F
A = SW1 , B = SW2 , C = SW3
F
= (ABC’) + (A’BC’)
= (BC’)(A + A’)
= (BC’)