I'm trying to simplify the following booleans:
Y = ¬A¬B¬C¬D + ¬A¬B¬CD + ¬A¬BC¬D + ¬A¬BCD + A¬B¬C¬D + A¬BC¬D + ABC¬D
The solution is:
Y = ¬A¬B + ¬B¬D + AC¬D
My solution is:
Y = ¬A¬B (¬C¬D + ¬CD + C¬D + CD) + A¬B¬C¬D + A¬BC¬D + ABC¬D
= ¬A¬B (¬C (¬D + D) + C (¬D + D)) + A¬B¬C¬D + A¬BC¬D + ABC¬D
= ¬A¬B (¬C + C) + A¬B¬C¬D + A¬BC¬D + ABC¬D
= ¬A¬B + A¬D (¬B¬C + ¬BC + BC)
= ¬A¬B + A¬D (¬B¬C + (¬BC + ¬BC) + BC) // law of idempotency
= ¬A¬B + A¬D (¬B (¬C + C) + C (¬B + B))
= ¬A¬B + A¬D (¬B + C)
= ¬A¬B + A¬B¬D + AC¬D
As you can see.. my answer varies with the solution by the 2nd term. Any ideas? Thanks.