Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 12: Q7E (page 828)

Design a circuit that implements majority voting for five individuals.

Short Answer

Expert verified

The result is \(abc + abd + abe + acd + ace + ade + bcd + bcd + bde + cde\).

Step by step solution

01

Defining of gates.

There are three types of gates.

It is also called NOT gate.

02

Construct a circuit.

A circuit that implements five inputs requires. Let the inputs are a, b, c, d ,e.

The outputs will need to be 1 when at least three of the inputs is a 1.Thus the outputs will be 1 when abc, abd ,abe, acd, ace, ade, bcd,bce, bde, or cde is equal to 1. Or equivalently when \(abc + abd + abe + acd + ace + ade + bcd + bcd + bde + cde\) I equal to 1

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Show that if \({\bf{F}}\) and \({\bf{G}}\) are Boolean functions represented by Boolean expressions in \({\bf{n}}\) variables and \({\bf{F = G}}\), then \({{\bf{F}}^{\bf{d}}}{\bf{ = }}{{\bf{G}}^{\bf{d}}}\), where \({{\bf{F}}^{\bf{d}}}\) and \({{\bf{G}}^{\bf{d}}}\) are the Boolean functions represented by the duals of the Boolean expressions representing \({\bf{F}}\) and \({\bf{G}}\), respectively. (Hint: Use the result of Exercise \(29\).)

Use the circuits from Exercises 10 and 11 to find the differenceof two four-bit integers, where the first integer is greater than the second integer.

Find the duals of these Boolean expressions.

\(\begin{array}{l}{\bf{a) x + y}}\\{\bf{b) \bar x\bar y}}\\{\bf{c) xyz + \bar x\bar y\bar z}}\\{\bf{d) x\bar z + x \times 0 + \bar x \times 1}}\end{array}\)

Show that \({\bf{x}} \oplus {\bf{y = y}} \oplus {\bf{x}}\).

Show that you obtain the absorption laws for propositions (in Table \({\bf{6}}\) in Section \({\bf{1}}{\bf{.3}}\)) when you transform the absorption laws for Boolean algebra in Table 6 into logical equivalences.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free