Overview: This article covers logic circuits in digital systems, focusing on combination circuits and encoders, their types, functions, and applications for efficient data processing. Logic circuits for digital systems may be combination or sequential.What is a combination circuit?A combination circuit is a memoryless digital circuit consisting of logic gates whose output is determined from only the present combination of inputs. It comprises an interconnection of basic logic gates NAND, NOR, or NOT gates to produce switching circuits.There are no feedback circuits in which changes to the input signal will immediately affect the output. They can be considered decision-making circuits that transform binary information with n inputs to required output data with m number of outputs. Common types of combination circuits includeAdderSubtractorComparatorMultiplexerDemultiplexerEncoderDecoderThe encoder-decoder structure is a popular approach in many deep learning applications, especially for sequence-to-sequence tasks. An overview of encoders is given in this article.What is an encoder?A binary encoder is a combinational circuit that converts information from  input lines into n-bit binary code. Only one input line is activated at a time, depending on which input is high, we get the specific code at the output.Types of EncodersThe most common types of encoders include4-to-2 Encoder8-to-3 Encoder (Octal Encoder)Decimal to BCD EncoderHexadecimal to Binary EncoderPriority Encoder4-to-2 EncoderConverts four input lines into two output lines, as shown in Fig. 1, applicable for data multiplexing and control signal generation. The block diagram of the 4-to-2 encoder is shown in Fig. 1, which converts = 4 input lines into n = 2 output lines.Fig. 1 Block diagram of 4:2 encoder. Source: Rakesh Kumar, Ph.D. Table. 1 Truth table of 4:2 encoder Source: Rakesh Kumar, Ph.D.DOD1D2D3XY100000010001001010000111 D0, D1, D2, and D3 are the input lines, and only one of these lines is active (1) at a time. X and Y are the output lines representing the binary code corresponding to the active input.The logical expression of 4:2 encoder can be derived from the truth table  asX = D2 + D3Y = D1 + D3The logic circuit of the 4:2 encoder can be implemented with the help of the OR gate, as shown in Fig. 2Fig. 2 Logic circuit diagram of 4:2 encoder. Source: Rakesh Kumar, Ph.D.8-to-3 Encoder (Octal Encoder)The octal encoder converts eight input lines into three output lines, often used for octal to binary conversion. The block diagram of the 8-to-3 encoder, in which it converts = 8 input lines into n = 3 output lines, is shown in Fig. 3.Fig. 3 Block diagram of 8:3 encoder. Source: Rakesh Kumar, Ph.D. Table. 2 Truth table of 8: 3 encoder. Source: Rakesh Kumar, Ph.D. DOD1D2D3D4D5D6D7XYZ1000000000001000000001001000000100001000001100001000100000001001010000001011000000001111 The logical expression of 8:3 encoder can be derived from the truth table asX = D4 + D5 + D6 + D7Y = D2 + D3 + D6 + D7Z = D1 + D3 + D5 + D7The logic circuit of the 8:3 encoder can be implemented with the help of the OR gate, as shown in Fig. 4Fig. 4 Logic circuit diagram of 8:3 encoder Source: GeeksforGeeksDecimal to BCD Encoder:Decimal to BCD encoder converts decimal numbers (0–9) into 4-bit Binary-Coded Decimal (BCD).Hexadecimal to Binary EncoderIt converts 16 input lines into four output lines, which is useful for hexadecimal to binary conversion.Priority EncoderA priority encoder is a unique encoder that prioritizes the input with the highest priority when two or more inputs are high simultaneously. The block diagram of the 4:2 priority encoder is shown in Fig. 5.Fig. 5 Block diagram of 4:2 priority encoder Source: Rakesh Kumar, Ph.D. Table. 3 Truth table of 4:2 priority encoder Source: Rakesh Kumar, Ph.D.DOD1D2D3XY100000X10001XX1010XXX111 The logic expression of the priority encoder can be derived from the truth table asX = D3 + D2Y = D3 + D2’D1AdvantagesBinary encoders encode input information into a compact code, effectively reducing the number of bits required to represent the input data. They enable efficient data handling in digital systems. Their ability to reduce the required input/output (I/O) pins makes them invaluable when connecting numerous input devices to microcontrollers or processors.To conclude, encoders are a significant component for many applications, including encoding data for transmission, providing motion feedback for robotics and machinery, converting user actions to digital signals, data multiplexing, and signal generation.Summarizing the Key PointsCombination circuits in digital systems consist of logic gates that produce outputs based on current input combinations without memory of past inputs.Encoders are essential in converting multiple input signals into a compressed binary code, significantly reducing electronic systems' required output lines.Priority encoders prioritize the highest active input when multiple signals are high, ensuring reliable data processing.ReferenceKalamani, C., Murugasami, R., Usha, S., & Saravanakumar, S. (2023). Design of encoder and decoder using reversible logic gates. Measurement Sensors, 31, 100989. https://doi.org/10.1016/j.measen.2023.100989Sofeoul-Al-Mamun, M., Miah, M. B. A., & Masud, F. A. (2017). A novel design and implementation of 8-3 encoder using Quantum-Dot Cellular Automata (QCA) technology. European Scientific Journal ESJ, 13(15), 254. https://doi.org/10.19044/esj.2017.v13n15p254Singha, T. B., Konwar, S., Roy, S., & Vanlalchaka, R. H. (2014). Power efficient priority encoder and decoder. International Conference on Computer Communication and Informatics, 1–5. https://doi.org/10.1109/iccci.2014.6921806ALL ABOUT ELECTRONICS. (2022a, May 1). Encoder in Digital Electronics | Working, application and Logic circuit of Encoder [Video]. YouTube. https://www.youtube.com/watch?v=NWiPVMDh7GEALL ABOUT ELECTRONICS. (2022, May 13). Priority Encoder Explained (with Simulation) | 4 to 2 Priority Encoder | 8 to 3 Priority Encoder [Video]. YouTube. https://www.youtube.com/watch?v=gnoqn705LBg