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Q15E

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Found in: Page 828

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# Use NAND gates to construct circuits with these outputs.$$\begin{array}{l}{\bf{a)}}\overline {\bf{x}} \\{\bf{b)x + y}}\\{\bf{c)xy}}\\{\bf{d)x}} \oplus {\bf{y}}\end{array}$$

The circuits are

(a)

(b)

(c)

(d)

See the step by step solution

## Step 1: Defining of gates.

There are three types of gates.

It is also called NOT gate.

(a)

## Step 3: Construct circuit by NAND.

(b)

Now,

$$\begin{array}{c}\overline {(\overline x + \overline y )} = \overline{\overline x} + \overline{\overline y} \\ = x - y\end{array}$$

## Step 4: Construct circuit for xy.

(c)

Now, $$\overline{\overline {x.y}} = x.y$$

## Step 5: Construct a circuit for $${\bf{x}} \oplus {\bf{y}}$$.

(d)

Now,

$$\begin{array}{c}(\overline x + y).(x + \overline y ) = \overline {(\overline x + y)} .\overline {(x + \overline y )} \\ = \overline{\overline x} .\overline y + \overline x .\overline{\overline y} \\ = x.\overline y + \overline x .y\\ = x \oplus y\end{array}$$

Therefore, by the circuits get the results.