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: Q8E (page 828)

Design a circuit for a light fixture controlled by four switches, where flipping one of the switches turns the light on when it is off and turns it off when it is on.

Short Answer

Expert verified

The result is\(\overline x yzw + x\overline y zw + xy\overline z w + xyz\overline w \).

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 four inputs requires. Let the inputs are x, y, z, w. And flipping one of the switches turns the light on when it is off and turns it off when it is on.

The outputs is\(\overline x yzw + x\overline y zw + xy\overline z w + xyz\overline w \).

Therefore, the outputs are\(\overline {\rm{x}} {\rm{yzw + x}}\overline {\rm{y}} {\rm{zw + xy}}\overline {\rm{z}} {\rm{w + xyz}}\overline {\rm{w}} \).

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

Use a \({\bf{K}}\)-map to find a minimal expansion as a Boolean sum of Boolean products of each of these functions in the variables \({\bf{w, x, y}}\) and \({\bf{z}}\).

\(\begin{array}{l}{\bf{a) wxyz + wx\bar yz + wx\bar y\bar z + w\bar xy\bar z + w\bar x\bar yz}}\\{\bf{b) wxy\bar z + wx\bar yz + w\bar xyz + \bar wx\bar yz + \bar w\bar xy\bar z + \bar w\bar x\bar yz}}\\{\bf{c) wxyz + wxy\bar z + wx\bar yz + w\bar x\bar yz + w\bar x\bar y\bar z + \bar wx\bar yz + \bar w\bar xy\bar z + \bar w\bar x\bar yz}}\\{\bf{d) wxyz + wxy\bar z + wx\bar yz + w\bar xyz + w\bar xy\bar z + \bar wxyz + \bar w\bar xyz + \bar w\bar xy\bar z + \bar w\bar x\bar yz}}\end{array}\)

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 \(29\).)

Express each of the Boolean functions in Exercise 3 using the operator \( \downarrow \).

Show that if \(F\) and \(G\) are Boolean functions of degree \(n\), then

\(\begin{array}{l}a)F \le F{\bf{ + }}G\\b)FG \le F\end{array}\)

Find the sum-of-products expansion of the Boolean function\({\bf{F}}\left( {{\bf{w, x, y, z}}} \right)\) that has the value 1 if and only if an odd number of w, x, y, and z have the value 1.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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