Electrical puzzle • Wires & Watts • Computer Chip Design • Circuit Design

Electrical puzzle

by Roger » Mon Feb 09, 2009 6:17 pm

Heres a puzzle you may have heard before which you can build as a simple electric circuit. First, the puzzle: a farmer is traveling to market with his cat, a chicken and some corn. He has to cross a river, and the only way to cross is in a small boat which can hold the farmer and just one of the three items he has with him. The problem is, he has to be very careful about what he chooses to leave behind at any time. If the cat and chicken are left alone, the cat will eat the chicken. If the chicken and the corn are left alone, the chicken will eat the corn. To solve the puzzle, you must show how the farmer can get himself and his three items across the river without losing any of them. The goal of this project is to design a simple electrical circuit that follows the puzzle. Youll need a 6 V battery, a flashlight bulb, a bulb holder, some connecting wire, and four toggle switches: 3 SPDT single-pole, double throw and 1 DPDT double-pole, double throw. Each switch represents one of the items: the farmer, the cat, the chicken and the corn you have to figure out which need to be SPDT switches and which one needs to be a DPDT switch. The switches are mounted on a small panel, in a horizontal row representing the river, which you can draw in. Each switch is labeled “Farmer”, “Cat”, “Chicken”, “Corn”. The circuit is to be designed so that if either of the problematic pairs cat-chicken, or chicken-corn are left alone on the same side of the river, the light bulb lights up, indicating an incorrect solution you can add a 6 V buzzer, too, if you like. Since the boat can hold only two items, players can use only two switches per “move”. Irwin Maths book, Wires and Watts: Understanding and Using Electricity has the solution Math, 1981, 67–70, but see if you can figure this one out on your own. The puzzle Ive got figured out but I am stuck on the wiring and cannot find an Irwin Math book.

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Digital Logic – Karnaugh Maps

Karnaugh Maps

Why Do You Need To Know About Karnaugh Maps?

What Is a Karnaugh Map?

Using Karnaugh Maps

Some Observations

Problems


Why Do You Need To Know About Karnaugh Maps?

        Karnaugh Maps are used for many small design problems.  It’s true that many larger designs are done using computer implementations of different algorithms.  However designs with a small number of variables occur frequently in interface problems and that makes learning Karnaugh Maps worthwhile.  In addition, if you study Karnaugh Maps you will gain a great deal of insight into digital logic circuits.

        In this section we’ll examine some Karnaugh Maps for three and four variables.  As we use them be particularly tuned in to how they are really being used to simplify Boolean functions.

        The goals for this lesson include the following.

  Given a Boolean function described by a truth table or logic function,

   Draw the Karnaugh Mapfor the function.
   Use the information from a Karnaugh Map to determine the smallest sum-of-products function.


What Does a Karnaugh Map Look Like?

        A Karnaugh Map is a grid-like representation of a truth table.  It is really just another way of presenting a truth table, but the mode of presentation gives more insight.  A Karnaugh map has zero and one entries at different positions.  Each position in a grid corresponds to a truth table entry.  Here’s an example taken from the voting circuit presented in the lesson on Minterms.  The truth table is shown first.  The Karnaugh Map for this truth table is shown after the truth table.

Boolean logic table for Electricity Puzzle