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–seven-segment decoder specified in Table.
(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 simplification. Compare the number of gate inputs with that obtained in part (b) and explain the difference.
Table Truth Table for BCD–to–Seven-Segment Decoder
BCD Input | Seven-Segment Decoder | |||||||||
A | B | C | D | a | b | c | d | e | f | g |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
All other inputs | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
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