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Logic circuits

4.2.5
Construct a simple logic circuit.

Of course, nothing is difficult for the person who doesn't have to do it.

invertors are not gates.

try this circuit at:

http://www.d-project.com/simcir/

Copyright © 1998-2000 Kazuhiko Arase

and see it working!

The simplified car alarm circuit.

 

 

 

 

 

 

 

 

 

 

 

(school-style democracy)

 

 

 

 

In an IB examination question, this would probably be enough.

 

Making a circuit only from NAND gates is not likely to be asked.

 

In the early days of electronics, NAND gates were simpler to fabricate than other types. So this was a common requirement.

You should construct the truth tables to see that this is so.

While I wouldn't expect this to come up in the exam, it does have only 3 inputs and consists of only 5 gates so you never know.

4.2.6

http://www.play-hookey.com/digital/

(quite good on digital electronics and other stuff too)

've seen this one before, but we will use it to illustrate an important point.

Fill in the map from the expression.

Again, you should construct the relevant truth tables to assure yourself that I'm not telling porkies .

(cockney rhyming slang - our non-UK readers might be a bit confused - google it)

 

on this page: [ circuits from expressions | expressions from circuits ]

Construct a circuit corresponding to an expression

A maximum of three inputs are to be expected and the circuits required are described as "simple" in the Subject Guide so this does not sound too difficult.

Consider an expression such as:

                            not A and B or A and not B

We are going to need two AND gates, an OR gate and a couple of invertors.

In the car alarm question we ended up with the expression:

                        A and not C or B and not C

At first glance we might seem to need 4-5 gates as well. However, by taking the common term out (using the distributive law) we see that only 3 are really needed:

This corresponds to the expression:

                       not C and (A or B)

A school committee consists of two students and a teacher chair. When voting for a course of action, either student and the teacher chair must support it. Derive the expression and construct the corresponding logic circuit using only NAND gates.

OK, let T = Teacher, S1 = Student1 and S2 = Student 2

So either student (an OR gate) AND the teacher produces a true:

                              outcome = T and (S1 or S2)

Yielding a circuit like this one:

To make a not gate from a nand gate, we tie the inputs together, like this:

So if we invert the output from a nand gate we should get an and gate. If we invert the inputs to a nand gate, we get an or gate.

Therefore the circuit looks like this:

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Expressions from Circuits

You can also be expected to look at a circuit and construct the equivalent boolean expression:

The expression is:

 not A and B or A and not B

Draw a quick Karnaugh map of this:

      B         A
0
1
         0    
         1    

The diagonal pattern of 1's is characteristic of XOR (exclusive OR gates). So the circuit and expression above could be simplified to:

                                                                 A xor B

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related: [ Topic 4 home | previous: karnaugh maps | next: more circuits ]

 


 
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