Question

Construct circuits from inverters, AND gates, and ORgates to produce these outputs.

\(\begin{array}{l}{\bf{a)}}\overline {\bf{x}} {\bf{ + y}}\\{\bf{b)}}\overline {{\bf{(x + y)}}} {\bf{x}}\\{\bf{c)xyz + }}\overline {\bf{x}} \overline {\bf{y}} \overline {\bf{z}} \\{\bf{d)}}\overline {{\bf{(}}\overline {\bf{x}} {\bf{ + z)(y + }}\overline {\bf{z}} {\bf{)}}} \end{array}\)

Short answer

The outputs are

1. The output is\(\overline {\rm{x}} {\rm{ + y}}\).
2. The output is\(\overline {{\rm{(x + y)}}} {\rm{x}}\).
3. The output is \({\rm{xyz + }}\overline {\rm{x}} \overline {\rm{y}} \overline {\rm{z}} \).

The output is \(\overline {{\rm{(}}\overline {\rm{x}} {\rm{ + z)(y + }}\overline {\rm{z}} {\rm{)}}} \).

Step-by-step solution

Defining of Gates.

There are three types of gates.

It is also called NOT gate.

Construct a circuit for \(\overline {\bf{x}} {\bf{ + y}}\).

(a)

Here the output is\(\overline {\rm{x}} {\rm{ + y}}\).

The output is the combination or NOT gate and OR gate. So, the circuit is

Plot a circuit for \(\overline {{\bf{(x + y)}}} {\bf{x}}\).

(b)

Here the output is\(\overline {{\rm{(x + y)}}} {\rm{x}}\).

Here the OR gate between x and y.And then a NOT gate after first step. Then AND gate between second step and x. So the circuit is

Draw a circuit for \({\bf{xyz + }}\overline {\bf{x}} \overline {\bf{y}} \overline {\bf{z}} \).

(c)

Here the output is \(xyz + \overline x \overline y \overline z \).

Here according to the outputs AND and OR gates are used. So, the circuit is

Construct a circuit of \(\overline {{\bf{(}}\overline {\bf{x}} {\bf{ + z)(y + }}\overline {\bf{z}} {\bf{)}}} \).

(d)

Here the output is \(\overline {(\overline x + z)(y + \overline z )} \).

The circuit is

Therefore, this is the require result.