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Digital circuits, both combinatorial and sequential, as well as Boolean algebraic number systems, are introduced in this course. It provides a perspective of the logic function design, going from the issue through the truth table. The combination of inputs is then what determines how to obtain a function. It allows pupils to create a circuit using gates that have been reorganized into packages. The student can construct various digital circuits, including encoders, transcoders, multiplexers, counters, registers, and memories, using the knowledge from this course. By transforming the problems into look-up tables and setting the input parameters and output parameters, it is possible to synthesize numerous decision-making processes. This course represents a sound basis for people in the case of vast integrated circuits because it provides the necessary tools to perform any numerical circuit.The essential points covered in this course are given as follows:Binary ArithmeticBinary, decimal, and hexadecimal systemsChange of basesThe different types of codesBinary arithmetic (addition, subtraction)The basic rules of digital logic gatesThe Logic functionsTruth and Karnaugh tables simplify logic functions.Encoders and decodersTranscoders (binary-Aiken, binary-Gray)The Seven-segment displaysMultiplexers and demultiplexersStudying the different flip-flopsSynchronous and asynchronous countersShift registers.Memories