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BCD to 7-Segment Decoder

Yunman Hao

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p>This paper mainly studies the effect of binary algorithm and truth table on digital circuit, and analyzes its logic circuit (from 0 to 9). Binary algorithm is used to make its truth table, draw the circuit diagram and make its PCB template.</p

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ORIGINAL ARTICLE

134 | Yunman Hao Electronics Science Technology and Application

BCD to 7-Segment Decoder

Yunman Hao*

University of Central Lancashire, Preston PR12HE, UK. E-mail: 2924527459@qq.com

Abstract: This paper mainly studies the effect of binary algorithm and truth table on digital circuit, and analyzes its lo g-

ic circuit (from 0 to 9). Binary algorithm is used to make its truth table, draw the circuit diagram and make its PCB

template.

Keywords: Circuit Design; Truth Table; 7-Segment Display; K-map; Experiment

1. Introduction of this experiment

With the development of science and technology,

the application field of diode is more and more extensive.

The main advantages of diode are small size, low price,

various colors, long service life, easy access, and easy

interface with various other digital circuits and electronic

components. Due to their small chip size, so many of

them can be connected together in a compact and small

package to produce, which is commonly referred to as

a 7-segment display. Therefore, we will study the work-

ing principles of decimal numbers displayed in

the 7-terminal decoder.

For the first step, we should convert the 4-bit code

into 7-bit control signal, so we drew the truth table which

is needed for the experiment (we made A the highest

position).

Table 1

Copyright © 2020 Yunman Hao

doi: 10.18686/esta.v7i4.160

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License

(http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium,

provided the original work is properly cited.

Electronics Science Technology and Application Volume 7 Issue 4 | 2020 | 135

The ten lines of the capital letter A, B, C, D in the

truth table represent Arabic numbers 0 to 9 respectively.

The lowercase letters a, b, c, d, e, f and g respectively

represent 7 LEDs that can emit light. When A is 1, it

means A is in an open state. When A is 0, it means A is

closed. When the number below the lowercase letter is 1,

the corresponding diode receives the signal, and the di-

ode lights up at this time. When its corresponding num-

ber is 0, the diode does not receive the signal, and the

diode turns off the lamp. The lowercase letters a, b, c, d,

e, f and g represent seven diodes respectively, and the

corresponding mode is shown in the following Figure 1.

Different codes can make different diodes light up to

form the numbers 0 to 9, thus completing the experi-

ment[1] .

We used K-map to simplify the code, and the most

simplified formula is the connection mode of the circuit.

Figure 1

2. Circuit design

The following formulas are the specific operation

results: ("*" is AND; "+" is OR )

Notice that: (A+C)!=A!*C!; (AC)!=A!+C!

a = A+C+BD+B!D!

=[( A+C+BD+B!D!)!]!

=[A!*C!*(BD+B!D!)!]!

=[A!*C!*(BD)!*(B!D!)!]!

This is my circuit design

：

And this circuit can test the state of "a" when we

enter any number from zero to nine. If we put 1 into this

circuit A is 0, B is 0, C is 0 and D is 1. It means A, B and

C are off but D is open. At this time, diode "a"

isn't bright. When we put 2 in the circuit, it means A is 0,

B is 0, C is 1 and D is 0. At this time, diode of "a"

is bright.

136 | Yunman Hao Electronics Science Technology and Application

Figure 2

Figure 3

Next is "b"：

b = A+A!B!+C!D!+CD

= [(A+A!B!+C!D!+CD)!]!

= [A!*(A!B!+C!D!+CD)!]!

= [A!*(A!B!)!*(C!D!+CD)!]!

= [A!*(A!B!)!*(C!D!)!*(CD)!]!

This is my circuit design:

When we open B and C, it means we enter the

number "6" into the circuit. At this time, diode "b" is

not bright. When we open B, it means we enter the num-

ber "4". At this time, diode "b" is bright.

Electronics Science Technology and Application Volume 7 Issue 4 | 2020 | 137

Figure 4

Figure 5

Next is "c":

c= B+A+D+C! =[(B+A+D+C!)!]!

=(B!*A!*D!*C)!

138 | Yunman Hao Electronics Science Technology and Application

This is my circuit design:

When I enter number 3, it shows:

Figure 6

When I enter number 2, it shows:

Figure 7

Notice that NAND=NOT+AND

Then is "d":

d = A+CD!+B!D!+C!DB+B!C

=[(A+CD!+B!D!+C!DB+B!C)!]!

=[A!*(CD!+B!D!+C!DB+B!C)!]!

=[A!*(CD!)!*(B!D!+C!DB+B!C)!]!

=[A!*(CD!)!*(B!D!)*(C!DB+B!C)!]!

=[A!*(CD!)!*(B!D!)*(C!DB)!*(B!C)!]!

Electronics Science Technology and Application Volume 7 Issue 4 | 2020 | 139

This is my circuit design:

When I enter number 7:

Figure 8

When I enter number 3:

Figure 9

140 | Yunman Hao Electronics Science Technology and Application

Next is "e":

e =B!D!+CD!+AB+AC

=[(B!D!+CD!+AB+AC)!]!

=[(B!D!)!*(CD!+AB+AC)!]!

=[(B!D!)!*(CD!)!*(AB+AC)!]!

=[(B!D!)!*(CD!)!*(AB)!*(AC)!]!

This is my circuit design:

When I enter number 4:

Figure 10

When I enter number 6:

Figure 11

Electronics Science Technology and Application Volume 7 Issue 4 | 2020 | 141

Next is "f":

f=A+C!D!+BC!+BD!

=[(A+C!D!+BC!+BD!)!]!

=[A!*(C!D!+BC!+BD!)!]!

=[A!*(C!D!)!*(BC!+BD!)!]!

=[A!*(C!D!)!*(BC!)!*(BD!)!]!

This is my circuit design:

When I enter number 4:

Figure 12

142 | Yunman Hao Electronics Science Technology and Application

When I enter number 1:

Figure 13

Final is "g":

g=A+BC!+B!C+CD!

=[(A+BC!+B!C+CD!)!]!

=[A!*(BC!+B!C+CD!)!]!

=[A!*(BC!)!*(B!C+CD!)!]!

=[A!*(BC!)!*(B!C)!*(CD!)!]!

This is my circuit design:

When I enter number 0:

Figure 14

Electronics Science Technology and Application Volume 7 Issue 4 | 2020 | 143

When I enter number 8:

Figure 15

3. The package diagram of the total

circuit

Now we have completed the operation of seven di-

odes. When these seven diodes are connected together,

the connection of the overall circuit is completed. The

specific connection method is shown in the following

Figure 16:

Figure 16

After the previous simplification and connection

circuit, we have obtained the connection mode of 7 di-

odes. We only need to connect these 7 circuits together to

obtain a total circuit. This circuit consists of NAND gate,

which can encode 4-bit signal into 7-bit 2-signal and

output it to the display. Note that the compilation in this

experiment uses binary numbers, only 0 and 1. When the

input signal is 1, the switch representing this position is

turned on, and the input terminal will generate an ele c-

trical signal and transmit it to the compiling part. After

compiling, the compiling result will be output to the co r-

responding diode, so that the seven diodes will be co m-

bined into a digital shape, and the experiment will be

completed[2] .

Let's give an example. When the switch A at the

signal input is open, B is closed, C is closed, and D is

open. The digital Europe that I choose is represented as

0110 in binary, which translates to 6 in decimal, that is, 6

should be A, C, D, E, F and G which are bright, and B is

not bright on the diode. In other words, the 0110 I input

will be transmitted to the 7 circuits I designed. These 7

circuits are equivalent to 7 decoders, which compile the

instruction 0110. The result of A compilation is 1, so A

is bright. The compilation result of bar is 0, so b is

not bright. The compilation results of c, d, e, f and g are

all 1, so the diodes c, d, e, f and g are all bright, and the

144 | Yunman Hao Electronics Science Technology and Application

corresponding signals are finally output to 7 correspond- ing diodes, forming the number 6.

Figure 17

Finally, because of the large volume of the main

store road, we packaged the circuit, reducing the volume

of the circuit and playing the role of protection[3]. Since

the NAND gate in my software was not packaged, the

package diagrams of 74LS00 and 74LS20 were selected

in the circuit diagrams I connected.

Figure 18

References

1. Tocci RJ, Widmer NS. Digital systems: Principles

and applications. 8th ed. New Jersey: Prentice Hall;

2000. p. 106– 262.

2. Nelson VP, Carroll BD, Nagle HT, et al. Digital

logic circuit analysis and design. 2nd ed. Prentice

Hall; 1995. p. 329– 346.

Electronics Science Technology and Application Volume 7 Issue 4 | 2020 | 145

3. Evens A. Logic of the digital. London: Bloomsbury Academic; 2017. p. 1– 192.

ResearchGate has not been able to resolve any citations for this publication.

  • Aden Evens

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