MultiplexorsSlide 2Slide 3Slide 4Slide 5Design ProcedureExampleSlide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41MultiplexersSlide 43Slide 44Combinational circuit implementation using MUXSlide 46Slide 47Slide 48Slide 49Example of MUX combo circuitSlide 51MultiplexorsAnd DecodersProf. Sin-Min LeeDepartment of Computer ScienceTwo-Level NAND Gate Implementation Example 1Two-Level NAND Gate Implementation Example 1Design Procedure•Determine the required number of inputs and outputs and assign letter symbols to them. •Derive the truth table that defines the required relationship between inputs and outputs. •Obtain the Boolean function. •Draw the logic diagram. •Verify the correctness of the design.Example•Design a circuit that converts a BCD codeword to its corresponding excess-3 codeword. We need 4 input variables and 4 output variables. Let us designate the 4 input binary variables by the symbols A, B, and C and D, and the four output variables by w, x, y, and z. The truth table relating the input and output variables is shown below:Note that the outputs for inputs 1010 through 1111 are don't care.Two-Lvel NOR Gate Implementation Example 2 eRichard HammingRichard Wesley Hamming, mathematician, pioneer computer scientist, and professor, died of a heart attack on January 7, 1998, in Monterey, California, at the age of 82. His research career began at Bell Laboratories in the 1940s, in the early days of electronic computers, and included the invention of the Hamming error-correcting codes. In the 1970s he shifted to teaching, and at his death he was Distinguished Professor Emeritus of computer science at the Naval Postgraduate School. He is survived by his wife Wanda, a niece, and a nephew.1948: Error Correction Error-detecting coding, first developed for telephone switching, is now used throughout the computing and telecommunications industries. In 1948 , R.W. Hamming (left) of Bell Labs developed a general theory for error-correcting schemes in which "check-bits" are interspersed with information bits to form binary words in patterns. When a single error occurs in transmission, the word becomes invalid, but the error is automatically located and corrected.Multiplexers•A combinational circuit that selects info from one of many input lines and directs it to the output line.•The selection of the input line is controlled by input variables called selection inputs.•They are commonly abbreviated as “MUX”.Combinational circuit implementation using MUX•We can use Multiplexers to express Boolean functions also.•Expressing Boolean functions as MUXs is more efficient than as decoders.•First n-1 variables of the function used as selection inputs; last variable used as data inputs.•If last variable is called Z, then each data input has to be Z, Z’, 0, or 1.Karnaugh Map Method of Multiplexer ImplementationConsider the function: A is taken to be the data variable and B,C to be the select variables.Example of MUX combo circuit •F(X,Y,Z) =
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