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.
Best Answer
I'm assuming a typo, when you said NAND-AND.
Essentially you must use the same method you used to transform AND - OR to NAND - NAND, but do it on terms.
$\overline C\ \overline D + A \overline B + A \overline D$, which is AND - OR. Take deMorgan's on full expression.
$\overline{\overline{ \overline C\ \overline D} \bullet \overline{A \overline B } \bullet \overline{A \overline D}}$, NAND - NAND. Now, take deMorgan's on terms.
$\overline{ ( C + D) \bullet (\overline A + B) \bullet (\overline A + D)}$ This is OR - NAND.
Finally, take deMorgan's on full expression.
If you keep going (alternating between full expression and terms), you would (8 steps) get back to the original expression.