How To Draw Truth Table From Boolean Expression

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TOPIC ane: Logic Representation

There are three common ways in which to represent logic.

i.  Truth Tables

2. Logic Circuit Diagram

3. Boolean Expression

We will discuss each herein and demonstrate ways to catechumen between them.

TOPIC two: Truth Tables

A truth table is a nautical chart of 1s and 0s arranged to indicate the results (or outputs) of all possible inputs.  The list of all possible inputs are arranged in columns on the left and the resulting outputs are listed in columns on the right.  There are 2 to the power n possible states (or combination of inputs).  For example with three inputs at that place are two^3=8 possible combination of inputs.  (Audio)

TOPIC 3: Logic Diagram

A logic diagram uses the pictoral description of logic gates in combination to represent a logic expression.  An instance below shows a logic diagram with three inputs (A, B, and C) and ane output (Y).  The interpretation of this will get articulate in the post-obit sections.

TOPIC four: Boolean Expression

Boolean Algebra tin can be used to write a logic expression in equation form.  At that place are a few symbols that you'll recognize merely need to redefine.

Note: Sometimes when the ! is used to correspond the NOT information technology is used earlier the letter and sometimes it is used later the letter.  Care should be used so that you understand which method is existence used!

Beneath is an example boolean expression.  In fact, it represents the aforementioned logic every bit the example logic circuit diagram above.  This concept will also become clearer when we embrace converting from and to the boolean expression beneath.

TOPIC five: Converting from a Logic Circuit Diagram to a Truth Table

This conversion is accomplished by selecting each state (or combination of inputs) one at a time, replacing the inputs with their respective values and figuring the value of each betoken through the excursion until the output is reached.   The final output value for each state is then listed in the truth tabular array next to the value of each input.  Below is a logic circuit diagram with the input values.  Written report it carefully for an extended period of time, it is an animated image and the inputs and output will change every few seconds.  (Click the image if information technology isn't changing)Below are the results of the conversion in truth table form.

TOPIC 6: Converting Logic Circuit Diagrams to Boolean Expressions

To convert from a logic excursion diagram to a boolean expression nosotros start by listing our inputs at the right place and procedure the inputs through the gates, i gate at a time, writing the outcome at each gate's output.  The following is the resulting boolean expression of each of the gates.

And hither is an example of the process beingness carried out.  The fact that the result simplifies to the XOR is merely coincidental. (Audio)

TOPIC 7: Converting Truth Tables to Boolean Expressions

In that location are 2 methods for converting truth tables to boolean expressions.

The Sum of Products (Audio)

The Product of Sums (Audio)

TOPIC 8: Converting Boolean Expressions to Logic Diagrams

Converting boolean expressions to logic diagrams is the most challenging conversion on this folio because it requires a very good understanding of guild of functioning.  Beneath is the order of operations used in this conversion. (Audio)

In lodge to complete this conversion nosotros will progress through the order of operations.  Nosotros will beginning look for bracketed quantities or something in parentheses.  Inside whatever parentheses nosotros will await for more than parentheses and so NOTs, then ANDs, then ORs.  It's best to begin with an example.

Audio

AudioAudioAudioSound TOPIC ix: Converting a Truth Table to a Logic Diagram

The easiest mode to achieve this is to kickoff catechumen the truth tabular array to a boolean expression and and so to a logic diagram.

You should at present be prepared to answer the following questions.  Click here for Webct.

1.  A logic system has 5 inputs.  How many possible states be in this system?

2.  What symbol is used to represent the NOT gate when the line over the letter is non convenient to use?

3.  A logic system has iii inputs and therefore 8 possible states.  The logic diagram representation is shown below.  Complete the truth table and convert the output column to hexadecimal if the state 0 is the least significant bit and the country 7 is the about meaning bit.

4.  Give the boolean expression from the above circuit diagram.

5.  A truth tabular array has the same states as in number 3 to a higher place.  However, the output column from top to bottom reads 00110101. Give the event of the sum of products method.

6.  Give the result of the product of sums method in number v above.

seven.  A boolean expression is given Y = (A+B)C+!BA+!C(A+B)+!(Air-conditioning).  But as in 3 higher up, produce a truth table and catechumen the output column to hexadecimal.

Source: https://drstienecker.com/tech-332/3-logic-circuits-boolean-algebra-and-truth-tables/

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