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Chapter 12: Q1E (page 827)

In Exercises 1–5 find the output of the given circuit.

Short Answer

Expert verified

The output of the circuit is\({\bf{(x + y)}}\overline {\bf{y}} \).

Step by step solution

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01

Defining of gates

There are three types of gates.

It is also called NOT gate.

02

Find the output.

The first gate is OR gate (x +y) and gate below is not. Therefore, the output is the AND combination of (x +y) and\(\overline {\bf{y}} \).

Therefore, the output of the circuit is\({\bf{(x + y)}}\overline {\bf{y}} \).

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Most popular questions from this chapter

In Exercises 1–5 find the output of the given circuit.

Explain how to build a circuit for a light controlled by two switches using \({\bf{OR}}\) gates, \({\bf{AND}}\) gates, and inverters.

Use a table to express the values of each of these Boolean functions.

\(\begin{array}{l}{\bf{a) F(x,y,z) = \bar z}}\\{\bf{b) F(x,y,z) = \bar xy + \bar yz}}\\{\bf{c) F(x,y,z) = x\bar yz + }}\overline {{\bf{(xyz)}}} \\{\bf{d) F(x,y,z) = \bar y(xz + \bar x\bar z)}}\end{array}\)

Show that the set of operators \(\left\{ {{\bf{ + , \cdot}}} \right\}\) is not functionally complete.

How many different Boolean functions \({\bf{F(x,y,z)}}\) are there such that \({\bf{F(\bar x,y,z) = F(x,\bar y,z) = F(x,y,\bar z)}}\) for all values of the Boolean variables \({\bf{x,y}}\), and \({\bf{z}}\)\({\bf{?}}\)
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