# (c) Simplify the following function using K-map: F(A, B, C, D) = Σ (1, 3, 4, 7, 11, 13) Draw the circuit for the resultant function using NAND gates.

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(c) Simplification using Karnaugh Map (K-map):

The given function is $$F(A, B, C, D) = \Sigma (1, 3, 4, 7, 11, 13)$$.

Let's construct the K-map:



$\begin{array}{cccc|c} AB\textbackslash CD & 00 & 01 & 11 & 10 \\ \hline 00 & 0 & 0 & - & 1 \\ 01 & - & 1 & 1 & - \\ \end{array}$



Groups:

- Group 1: $$D'C' = 1$$

- Group 2: $$BC = 1$$

- Group 3: $$AD = 1$$

The simplified expression is $$F(A, B, C, D) = D'C' + BC + AD$$.

Circuit using NAND Gates:

The NAND gate implementation for the simplified expression is as follows:

- $$D_1 = \overline{D'}$$

- $$C_1 = \overline{C'}$$

- $$C_2 = \overline{B}$$

- $$A_1 = \overline{A}$$

The circuit:



+-------+

|       |

A ----( NAND )--- D1 ---- F

|       |

B ----( NAND )--- C2

|       |

C ----( NAND )--- C1

|       |

D ----( NAND )--- A1

|       |

+-------+



This circuit uses NAND gates to implement the simplified Boolean expression $$F(A, B, C, D) = D'C' + BC + AD$$.