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Q15E

Expert-verifiedFound in: Page 828

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)

**There are three types of gates.**

**It is also called NOT gate.**

(a)

** **

(b)

** **

Now,

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

(c)

** **

Now, \(\overline{\overline {x.y}} = x.y\)

(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.

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