University of Bridgeport by 5IB3dq2k

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									                                         University of Bridgeport
                              Department of Computer Science and Engineering

                                                   CpE 315
                                    Digital Systems Design II - Handout #2

Combinational logic example - design of a 2-bit multiplier

                 TRUTH TABLE

        A   B    C   D      W   X    Y   Z
        0   0    0   0      0   0    0   0                    A
        0   0    0   1      0   0    0   0                    B                                      W
        0   0    1   0      0   0    0   0                                      2-bit                X
        0   0    1   1      0   0    0   0                                    multiplier             Y
        0   1    0   0      0   0    0   0                    C                                      Z
        0   1    0   1      0   0    0   1                    D
        0   1    1   0      0   0    1   0
        0   1    1   1      0   0    1   1
        1   0    0   0      0   0    0   0
        1   0    0   1      0   0    1   0                             Using K-maps:
        1   0    1   0      0   1    0   0                                                    _     _
        1   0    1   1      0   1    1   0                             W = ABCD          X = ABC + ACD
        1   1    0   0      0   0    0   0                                 _       _    _      _
        1   1    0   1      0   0    1   1                             Y = ABC + BCD + ACD + ABD
        1   1    1   0      0   1    1   0
        1   1    1   1      1   0    0   1                             Z = BD


        Now let's use MUXes: use one for each output - can be 16 to 1, 8 to 1 or 4 to 1

        Connect system data inputs to the MUX data selects and find the MUX data inputs




        Can also use a decoder to implement the multiplier: here we use a 4 to 16 decoder and 4
                     OR shapes (one for each output) - connect system inputs to the decoder inputs

								
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