**(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 \(F(A, B, C, D) = D'C' + BC + AD\).

## 0 टिप्पणियाँ:

## Post a Comment