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Minimum SOP and POS
15%kmapboolean-algebraA combinational circuit has four inputs a, b, c, d, read together as a 4-bit number with a as the most-significant bit. The output must be 1 when the input value is 2, 7, or 15, and 0 when it is 0, 1, 4, 5, 6, 9, 10, 13, or 14. Input values 3, 8, 11, and 12 can never occur, so they are don't-cares. As a K-map:
| a'b' | a'b | ab | ab' | |
|---|---|---|---|---|
| c'd' | 0 | 0 | d | d |
| c'd | 0 | 0 | 0 | 0 |
| cd | d | 1 | 1 | d |
| cd' | 1 | 0 | 0 | 0 |
Derive the minimum sum-of-products form and drive it on out_sop, and the minimum product-of-sums form and drive it on out_pos.
For grading, treat the don't-cares as follows (the values both minimal forms produce): input values 3 and 11 are 1; input values 8 and 12 are 0. With these choices the minimum SOP and minimum POS describe the same fully-specified function, so out_sop and out_pos must agree on every input.