Complete the design of the BCD–to–seven-segment decoder by performing the following steps:

(a) Plot the seven maps for each of the outputs for the BCD–to–sevensegment decoder speciied in Table 3-9.

Table 3-9

(b) Simplify the seven output functions in sum-of-products form, and determine the total number of gate inputs that will be needed to implement the decoder.

(c) Verify that the seven output functions listed in the text give a valid simpliication. Compare the number of gate inputs with that obtained in part (b) and explain the difference.

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Truth Table for BCD-to-Seven-Segment Decoder BCD Input A B C D 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 All other inputs 1 1 1 0 0 1 0 0 a Seven-Segment Decoder defg 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 b 1 0 10 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 00 1 1 0 0 1 1 0 0 0 0 1 0 1