Analysis and Research on Display Decoder Design in Digital Circuit

Abstract: In view of the problem that input and output variables are difficult to determine when designing a display decoder, a functional analysis and variable association design method is proposed. The output of the display decoder is driven by a driver to make the display work. The number and state of the output variables depend on the type of display, and the number and state of the input variables are related to the output display results. Research shows that the number of bits of the input variables of the display decoder, n, and the number of output display results N satisfy 2n=N or 2n-1 Keywords: decoder; driver; display design; input variables; output variables

The display decoder is a very important device in the combinational logic circuit of digital electronic technology. It is indispensable in the application of digital electronic technology, especially in today's digital information technology. Its application is becoming more and more extensive. However, when organizing scientific and technological innovation and electronic design and production competitions, students are always confused about how to accurately design a display decoder that meets the functional requirements when designing and producing electronic products such as buzzers, scorers, and timers. This paper analyzes and studies this problem.

1 Functions and types of display decoders
The logic circuit that realizes the decoding function is a decoder. Decoding is the reverse process of encoding. In a digital system, any information or data, whether it is text, numbers, symbols or graphics, must be converted into binary code during monitoring, control, and transmission. This is encoding; and during or at the end of monitoring, control, and transmission, the corresponding information processing results must be displayed, which requires the binary code to be restored to the corresponding text, numbers, symbols or graphics. This process is decoding. In digital electronic technology, there are two types of decoders, namely variable decoders and display decoders.
Variable decoders are divided into binary and non-binary types. A binary decoder is a decoder in which the number of bits n of the input binary code and the number N of the decoded restored output information is N=2n. A non-binary decoder is a decoder that cannot meet this relationship.
The display decoder displays text, numbers, symbols, etc. The display materials include fluorescent, liquid crystal, LED, etc. The display forms include segmented, overlapping, dot matrix, etc., and the working modes include common cathode and common anode, etc.
Whether it is a variable decoder or a display decoder, there are some commonly used stereotyped products, such as a three-line to eight-line binary decoder, that is, input three binary codes and output eight information, satisfying 23=8. The commonly used integrated chips are the 74 series and the 54 series, the most typical chip is the 74LS138, and the most typical display decoder is a non-binary decimal number decoder, the model is 74LS48. However, in practical applications and innovative designs, these products are not enough to meet the requirements of different functions, and new display decoders must be designed. In the design process, the most problematic is the determination of input and output variables when designing display decoders.

2 Design steps of display decoders
Display decoders belong to the combinational logic circuit in digital electronic technology, so when designing, the design method of combinational logic circuits should also be followed. There are four steps: first, determine the meaning of the input and output variables and their states of the designed circuit according to the functional requirements; second, list the truth table according to the functional requirements; third, use the Karnaugh map to simplify and obtain the logical expression of the input and output variables; fourth, draw a logic diagram based on the logical expression.
From previous teaching practice, skill competitions and extracurricular activities, it is found that in the four steps of combinatorial logic circuit design, the difficulty of designing each type of circuit is different. For example, when designing a combinatorial logic circuit with input and output variables that conform to binary relations, the most critical step is to list the truth table according to the functional requirements in the second step; when designing a combinatorial logic circuit with non-binary characteristics, the focus is to grasp the third step of Karnaugh map simplification with constraints; when the design requires the use of specified components to implement the combinatorial logic circuit, the design difficulty is the fourth step, and the simplified logical expression must be converted into a functional relationship that can be implemented with specified components according to the design requirements, and then the logic diagram is drawn; then when designing a display decoder, the most confusing and unclear step is the first step in the design process.

3 Design skills of display decoders
According to the design method of combinatorial logic circuits, aiming at the characteristics of display decoders, combined with the outstanding problems in design practice, the first step in the design process of display decoders is analyzed and studied, and the skills and methods for accurately determining the input and output variables of the designed circuit are obtained.

First of all, we need to understand the role of the display decoder in the digital circuit and confirm its functional relationship in the display circuit, as shown in Figure 1. From the figure, we know that the digital display circuit is composed of a display decoder, a display driver and a result display. The display decoder is to decode the binary code after monitoring, control and transmission in the digital circuit, restore it into corresponding text, numbers, symbols and other information, and display it in different forms; the display driver is a circuit to ensure the normal operation of the result display. According to the different materials, power and circuits of the result display, it adopts a variety of methods such as current limiting resistor drive, Darlington drive and relay drive; there are many types of display content and methods, and the most common finalized product is the seven-segment digital display tube. Therefore, when designing a display decoder, it is necessary to take into account the three parts of the decoder, driver and display.

3.1 Determine input variables based on display results
The key and difficulty of display decoder design is to determine the input and output variables and their number. Through practice, it is known that the input variables of the display decoder should be determined according to the number of output results of the display decoder. In other words, no matter what form (text, numbers, symbols) and mode (common cathode or common anode) of the display used by the display decoder, and no matter what content it displays, as long as the number of displayed results is the same (both of them need to display 4 numbers), then the input variables of the designed decoder are the same, that is, the output result N=4, 4=22=2n, so the input variable is n=2.
If you want to design a decoder that displays the letters "E, L, H, F", it is obvious that there are 4 output results, that is, N=4=22=2n, so the input variable is also n=2.
If the output display result does not satisfy N=2n with the input, for example, in every level of the TV program "Avenue of Stars", the host can be heard saying the result by counting down five. If the audience says 5, 4, 3, 2, 1 in unison, and the electronic display is added, wouldn't it be more scientific and intuitive? Because there are five output results, N=5≠2n, in this relationship, the output variable N does not satisfy N=2n with the input variable n, which has the characteristics of non-binary. According to the corresponding relationship between the input and output of the combinational logic circuit, the output result N of this display decoder and the input variable n should satisfy 2n-1 From the above analysis, it can be concluded that the number of input variables of the display decoder depends on the number of output results, that is, the number of output results N and the number of bits of the input variable n satisfy N=2n or 2n-1

3.2 Determine output variables according to display form
After determining the input variables, the output variables should be designed according to the functional requirements. How many output variables are needed? After repeated research, it is concluded that the output variables are determined by the type of display selected. For example, if you want to design a display decoder that displays the numbers 5, 4, 3, 2, 1 and a display decoder that displays the letters E, L, H, F, although the content and number of the two display results are different, if both circuits use seven-segment digital tubes, then the number of output variables of the two decoding circuits is 7. If the circuit that displays the letters E, L, H, F uses a five-stroke display, then its output variables are only 5.

It can be seen that the number of display decoder output variables depends only on the form of the selected display, whether it is text, symbols, digital, or segmented, overlapping, or dot matrix display, which is determined by the designer. If the segmented display E, L, H, F is selected, then the number of decoder output variables is the number of segments of the display, and has nothing to do with the output display content and the number of display results, as shown in Figures 2 and 3.

3.3 Determine the variable state according to the display mode
After determining the input and output variables of the design display decoder, in order to accurately design the truth table, it is also necessary to clarify the corresponding relationship between the state of each variable and the decoding restoration, which determines the entire design process.
For the input variables, the n-bit binary code combination value can be designed in an increasing or decreasing order with the output result N one by one, as shown in Table 1 and Table 2.
If the input conforms to the characteristics of binary, it is sufficient to determine the corresponding relationship between all code combinations and outputs. If it does not conform to the binary correspondence, the redundant input combinations must be constrained to ensure the realization of the function. For example: design a decoder that displays the letters E, L, H, and F. The two-bit binary code input has four combinations, namely 00, 01, 10, and 11. Let them correspond to the output display results E, L, H, and F one by one (or in reverse order) and decode and restore them, as shown in Table 1. The design displays the numbers 5, 4, 3, 2, and 1. The input is a three-digit binary code, and its combinations are 000, 001, 010, 011, 100, 101, 110, and 111, respectively. The output result only uses five combinations. The designer determines which five combinations to use, whether to use the first five or the last five, or to use five combinations whose binary code combination values ​​are consistent with the decimal values, as shown in Table 2.
Whether the output variable is high or low level effective depends mainly on whether the display used is a common cathode or a common anode. If the output uses a common cathode display, the output is high level effective; if the design output is low level effective, a common anode display should be used.
It can be seen that the corresponding relationship between the state of the input and output variables and the decoding restoration is completely determined by the designer according to the habits and working mode of the display, which provides a platform and conditions for designers to design and produce flexibly, independently, and innovatively.

4 Design cases of display decoders
4.1 Design a display decoder that uses a five-stroke display to display the letters E, L, H, and F
This is a design task that specifies the display form (the five strokes are shown in Figure 2), but does not limit its working mode to common cathode or common anode. According to the design steps and the above analysis, first determine that the design circuit has two input variables A and B, and the four input combinations correspond to the output of four displayed letters, and five output variables. A common anode display is selected, so the output low level is valid. Secondly, list the corresponding truth table according to the functional requirements, as shown in Table 1. Then use the Karnaugh map to simplify the expression. From the truth table, it can be seen that the input of this design circuit uses positive logic and the output is negative logic. Therefore, the output obtained by the Karnaugh map simplification is the inverse variable, as shown in Figure 4, and the remaining outputs are simplified in the same way. Finally, draw a logic diagram based on the expression, which is the same as other designs and will not be repeated.

4.2 Design a display decoder that uses a common cathode seven-segment digital tube to display the numbers 5, 4, 3, 2, 1
In this design, not only is the display limited to a seven-segment digital display tube (as shown in Figure 3), but the display also works in a common cathode mode, that is, the output is high level valid. At the same time, the input and output do not satisfy 2n=N, so some input combinations are redundant and need to be selected and set, which provides great flexibility and innovation for designers.
According to the design techniques and settings of the display decoder described in this article, this display decoder has three inputs A, B, C, and seven outputs Ya, Yb, Yc, Yd, Ye, Yf, and Yg. Its truth table is shown in Table 2. The redundant outputs in the table are not displayed, or they are used as function expansion control terminals (readers study on their own). In the subsequent Karnaugh map simplification, attention should be paid to the processing of constraint items, and the drawing of logic diagrams will not be repeated.
It is particularly emphasized that when the display decoder is designed and confirmed to achieve its functional requirements through simulation, when it is actually connected to the display, it is necessary to select a suitable driver as a bridge and link according to the display type, power and other technical indicators to ensure the normal operation of the display.

5 Conclusion
Display decoders are increasingly widely used in the field of digital electronic technology. Accurately and flexibly mastering their design methods has laid a solid theoretical foundation for the comprehensive use of EDA technology, single-chip microcomputer technology, and embedded technology to develop new electronic products, and provided an effective reference and foundation for cultivating and improving innovative design capabilities.