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This is the boolean function: F(A,B,C,D) = Σ (0,4,8,9,10,11,12,14) and so after using a K-map to minimize it, I came out with F(A,B,C,D) = C'D' + AB' + AD'. Now the other two parts of the problem were representing it with AND-NOR gates and NAND-AND gates which I knew how to do. How do I do it with OR-NAND gates and NOR-OR gates?

Do I simply look for 0's in the karnaugh map and write a minimized boolean expression for 0's and then negate it? I'm very much confused by how to do this with OR and NAND gates. Any help appreciated.

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Using the distributive properties of NOT,

C'D' + AB' + AD' = (C+D)' + (A'+B)' + (A'+D)'

C'D' + AB' + AD' = ((C+D)(A'+B)(A'+D))'

The inner parentheses use OR gates and the outer is a NAND

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    \$\begingroup\$ Perfect. Looks like I was making it more complicated than it needed to be. Do you have any ideas about NOR-OR? \$\endgroup\$ Commented Mar 11, 2016 at 15:10
  • \$\begingroup\$ yup, just use the end of the first step above (C+D)' is a NOR, (A'+B)' is another, and (A'+D)' is the third. Then just OR them together. \$\endgroup\$ Commented Mar 11, 2016 at 16:16

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