Reduce F (A, B, C, D) = ∑ (1, 3, 4, 5,6, 7, 9, 11, 12, 13, 14, 15)using K-Map and implement it using nandgates only.

Sure, let's start by creating a Karnaugh Map (K-Map) for the given function F(A, B, C, D).

The K-Map will be a 4x4 grid, representing all possible combinations of A, B, C, and D. We will fill in the cells corresponding to the minterms given in the sum of products expression.

Next, we will group the 1s in the K-Map. We will try to make the groups as large as possible, and each group must be a rectangle (which can be a square) and the number of cells in the group must be a power of 2.

After grouping, we will write the Product of Sum (POS) expression for each group. The variables that remain constant in a group will be part of the product term for that group.

Finally, we will sum all the product terms to get the simplified expression for the function F(A, B, C, D).

Now, to implement this function using only NAND gates, we will use the fact that a NAND gate can be used to perform all three basic logic operations: AND, OR, and NOT.

• To perform a NOT operation using a NAND gate, we connect both inputs of the NAND gate to the variable we want to invert.
• To perform an AND operation using a NAND gate, we first connect the inputs of the NAND gate to the variables we want to AND together, and then we connect the output of this NAND gate to both inputs of a second NAND gate to invert it back.
• To perform an OR operation using NAND gates, we first invert each of the variables we want to OR together using a NAND gate, and then we connect the outputs of these NAND gates to the inputs of a third NAND gate.

By combining these operations, we can implement the simplified function using only NAND gates.