http://openbookproject.net/books/socratic/output/display_instructor.pdf. It's a snapshot of the page taken as our search engine crawled the Web.
The web site itself may have changed. You can check the current page or check for previous versions at the Internet Archive. Yahoo! is not affiliated with the authors of this page or responsible for its content.
Digital display circuits Digital display circuits
This worksheet and all related les are licensed under the Creative Commons Attribution License,
version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/, or send a
letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. The terms and
conditions of this license allow for free copying, distribution, and/or modication of all licensed works by
the general public.
Resources and methods for learning about these subjects (list a few here, in preparation for your
research):
1 Question 1
What is the purpose of a seven-segment decoder circuit? What is a seven-segment display, and why
do we need a decoder circuit to drive it? Research the part number for a typical seven-segment decoder
circuit (either CMOS or TTL).
le 01417
Answer 1
Seven-segment displays are a very common numerical interface for digital electronic equipment:
Seven-segment
display
a
b
c
d
e
f
g
COM
A special decoder circuit is needed to translate 4-bit BCD codes into the particular combinations of
segment activations that represent decimal digits.
Follow-up question: what does the internal schematic of a typical seven-segment display look like? Is
there just one type, or are there dierent types of seven-segment displays?
Notes 1
Be sure to ask your students to reveal the decoder datasheets they found. Once again, manufacturer
datasheets contain a wealth of information, and your students will learn much by researching them.
2 Question 2
A seven segment decoder is a digital circuit designed to drive a very common type of digital display
device: a set of LED (or LCD) segments that render numerals 0 through 9 at the command of a four-bit
code:
Seven-segment display
a
b
c
d
e
f
g
A
B
C
D
a
b
c
d
ef
g
Display driver IC
V
DD
. . .
. . .
. . .
. . .
. . .
. . .
. . .
Inputs
The behavior of the display driver IC may be represented by a truth table with seven outputs: one for
each segment of the seven-segment display (a through g). In the following table, a 1 output represents an
active display segment, while a 0 output represents an inactive segment:
D
C
B
A
a
b
c
d
e
f
g
Display
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
3
0
1
0
0
0
1
1
0
0
1
1
4
0
1
0
1
1
0
1
1
0
1
1
5
0
1
1
0
1
0
1
1
1
1
1
6
0
1
1
1
1
1
1
0
0
0
0
7
1
0
0
0
1
1
1
1
1
1
1
8
1
0
0
1
1
1
1
1
0
1
1
9
Write the unsimplied SOP or POS expressions (choose the most appropriate form) for outputs a, b, c,
and e.
le 02824
3 Answer 2
Raw (unsimplied) expressions:
a
= (D + C + B + A)(D + C + B + A)
b
= (D + C + B + A)(D + C + B + A)
c
= D + C + B + A
e
= D C B A + D CBA + DCBA + DC B A
Challenge question: use the laws of Boolean algebra to simplify each of the above expressions into their
simplest forms.
Notes 2
This shows a very practical example of SOP and POS Boolean forms, and why simplication is necessary
to reduce the number of required gates to a practical minimum.
4 Question 3
A seven segment decoder is a digital circuit designed to drive a very common type of digital display
device: a set of LED (or LCD) segments that render numerals 0 through 9 at the command of a four-bit
code:
Seven-segment display
a
b
c
d
e
f
g
A
B
C
D
a
b
c
d
ef
g
Display driver IC
V
DD
. . .
. . .
. . .
. . .
. . .
. . .
. . .
Inputs
The behavior of the display driver IC may be represented by a truth table with seven outputs: one for
each segment of the seven-segment display (a through g). In the following table, a 1 output represents an
active display segment, while a 0 output represents an inactive segment:
D
C
B
A
a
b
c
d
e
f
g
Display
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
3
0
1
0
0
0
1
1
0
0
1
1
4
0
1
0
1
1
0
1
1
0
1
1
5
0
1
1
0
1
0
1
1
1
1
1
6
0
1
1
1
1
1
1
0
0
0
0
7
1
0
0
0
1
1
1
1
1
1
1
8
1
0
0
1
1
1
1
1
0
1
1
9
A real-life example such as this provides an excellent showcase for techniques such as Karnaugh mapping.
Lets take output a for example, showing it without all the other outputs included in the truth table:
D
C
B
A
a
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
Plotting a Karnaugh map for output a, we get this result:
5 00
01
11
10
00 01 11 10
1
1
0
0
1
1
1
1 1
1
DC
BA
Identify adjacent groups of 1s in this Karnaugh map, and generate a minimal SOP expression from
those groupings.
Note that six of the cells are blank because the truth table does not list all the possible input
combinations with four variables (A, B, C, and D). With these large gaps in the Karnaugh map, it is
dicult to form large groupings of 1s, and thus the resulting minimal SOP expression has several terms.
However, if we do not care about output as state in the six non-specied truth table rows, we can ll
in the remaining cells of the Karnaugh map with dont care symbols (usually the letter X) and use those
cells as wildcards in determining groupings:
00
01
11
10
00 01 11 10
1
1
0
0
1
1
1
1 1
1
DC
BA
With this new Karnaugh map, identify adjacent groups of 1s, and generate a minimal SOP expression
from those groupings.
le 02838
6 Answer 3
Karnaugh map groupings with strict 1 groups:
DB
+ DCA + DC B + C B A
00
01
11
10
00 01 11 10
1
1
0
0
1
1
1
1 1
1
DC
BA
Karnaugh map groupings with dont care wildcards:
D
+ B + CA + C A
00
01
11
10
00 01 11 10
1
1
0
0
1
1
1
1 1
1
DC
BA
Follow-up question: this question and answer merely focused on the a output for the BCD-to-7-segment
decoder circuit. Imagine if we were to approach all seven outputs of the decoder circuit in these two
fashions, rst developing SOP expressions using strict groupings of 1 outputs, and then using dont care
wildcards. Which of these two approaches do you suppose would yield the simplest gate circuitry overall?
What impact would the two dierent solutions have on the decoder circuits behavior for the six unspecied
input combinations 1010, 1011, 1100, 1101, 1110, and 1111?
Notes 3
One of the points of this question is for students to realize that bigger groups are better, in that they yield
simpler SOP terms. Also, students should realize that the ability to use dont care states as wildcard
placeholders in the Karnaugh map cells increases the chances of creating bigger groups.
Truth be known, I chose a pretty bad example to try to make an SOP expression from, since there are
only two non-zero output conditions out of ten! Formulating a POS expression would have been easier, but
thats a subject for another question!
7 Question 4
Examine the datasheet for a 7447 BCD-to-7-segment decoder/driver IC, and identify what input
conditions need to be met in order to cause it to display any decimal digit from 0 to 9.
le 03039
Answer 4
Ill let you gure out these details by researching the datasheet yourself!
Follow-up question: what features dierentiate the 7447 decoder/driver IC from the 7448 or 7449?
How about the 74247, 74248, and 74249 decoder/driver circuits? Be prepared to show your sources when
answering this question in class.
Notes 4
Given that datasheets for this particular decoder/driver IC are easy to obtain and read, your students
should have no trouble doing the research.
8 Question 5
Two electronics students attempt to build 7-segment display circuits, one using a 7447 decoder/driver
IC and the other using a 7448. Both students connect their ICs to common-cathode 7-segment displays as
such:
Seven-segment display
A
B
C
D
a
b
c
d
ef
g
Display driver IC
V
DD
Inputs
a
b
c
d
e
f
g
744x
The student using the 7448 notices the LED segments glowing faintly, but the patterns are not correct
for the digits that are supposed to be displayed. The student using the 7447 has an even worse problem:
no light at all! Both have checked and re-checked their wiring, to no avail. It seems as though all the
connections are in the right place.
What do you think the problem is? Hint: consult datasheets for both chips to nd clues!
le 03916
Answer 5
Neither the 7447 nor the 7448 are designed to source current to the LED segments, only sink current.
Ill let you gure out why the 7448 chip has the ability to make any of the LED segments light up at all.
Follow-up question: trace the direction of electron ow through the wires between the decoder chip and
the display.
Notes 5
This question provides an excellent opportunity to discuss the dierence between sourcing and sinking
current, as well as the importance of knowing what the output stage of an IC looks like internally.
9 Question 6
An obsolete display technology that still nds enthusiastic followers in the hobbyist world, called Nixie
tubes
, relies on a BCD-to-10 decoder to drive one of ten dierent metal cathodes inside a neon-lled glass
bulb. For each BCD code, exa