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Convert the following expressions to canonical Product-of-Sum form(a) (A + C)(C + D)(b) (X + Y)(Y + Z)(X + Z) |
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Answer» (a) (A + C)(C + D) = (A + BB’ + C + DD’)(AA’ + BB’ + C + D) = (A + B + C + D)(A + B’ + C + D’)(A + B + C + D)(A’ + B’ + C + D) By removing duplicate terms we get canonical Product-of-Sum form: (A + B + C + D)(A + B’ + C + D’)(A’ + B’ + C + D) F = π(0, 5 , 12) F = M0 + M5 + M12 (b) (X + Y)(Y + Z)(X + Z) = (X + Y + ZZ’)(XX’ + Y + Z)(X + YY’ + Z) = (X + Y + Z)(X + Y + Z’)(X + Y + Z)(X’ + Y + Z)(X + Y + Z)(X + Y’ + Z) By removing duplicate terms we get canonical Product-of-Sum form: (X + Y + Z)(X + Y + Z’)( X’ + Y + Z)( X + Y’ + Z) F = π(0, 1 , 2, 4) F = M0 + M1 + M2 + M4 |
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