# How to construct a truth table with 1 and 0

• Her-0
In summary, to set up the truth table for a circuit function, you will need to create 5 columns: one for each input (W, X, Y, Z) and one for the output (F). Then, using Boolean algebra, substitute the binary values for each input in the circuit function and evaluate the expression to determine the output for each input combination.
Her-0
I have written the function for the circuit as --> F= (W'.Z)(X.Y')+(Y'+X)+(Z+W)

I am very confused on how to set up the truth table can someone help me?

Her-0 said:
I have written the function for the circuit as --> F= (W'.Z)(X.Y')+(Y'+X)+(Z+W)

I am very confused on how to set up the truth table can someone help me?

You appear to have 4 inputs and one output. Make your table with 5 columns, with the 1st 4 columns counting binary, and the 5th column with the result for each combination of inputs

0000 F(0000)
0001 F(0001)
etc...

berkeman said:
You appear to have 4 inputs and one output. Make your table with 5 columns, with the 1st 4 columns counting binary, and the 5th column with the result for each combination of inputs

0000 F(0000)
0001 F(0001)
etc...

So what you are saying is set up 5 columns W,X,Y,Z than the last as F but how would I come about calculating the result that's what I am confused at.

Assume you had just 2 variables: X and Y, there would be 4 combinations for them:
(0,1), (1,0), (1,1), (0,0)

Let's assume your function was X and Y, so figure out what would T and T = ? T and F = ? , etc.

NoMoreExams said:
Assume you had just 2 variables: X and Y, there would be 4 combinations for them:
(0,1), (1,0), (1,1), (0,0)

Let's assume your function was X and Y, so figure out what would T and T = ? T and F = ? , etc.

Okay, but than what about if its an and/or the values would differ
For and:
X Y
T T T
T F F
F T F
F F F

For or:
X Y
T T T
T F T
F T T
F F F

Yes so you would have shown that X and Y is not logically equivalent to X or Y which you should've known.

I'll work with 1's and 0's. It's easier to read the symbols. As for evaluating the logic expression, you have to work with certain results from Boolean algebra.

Take this as an example:
Suppose the configuration from a particular line in your truth table is 1101 which is an ordered input for WXYZ. Then after substituting the Boolean values for W,X,Y,Z the Boolean expression becomes (0*1)(1*1)+(1+1)+(1+1) where * denotes AND and + denotes OR.

Evaluate this in order of parantheses:
(0*1) = 0, (1*1)=1, 1+1=1, 1+1=1

so it now becomes: 0*1+1+1 = 0+1+1 = 1.

So for that particular input configuration F=1. Now apply this method to all the other possible inputs for WXYZ and you have the truth table.

## 1. What is a truth table and why is it important in science?

A truth table is a table that shows all possible combinations of inputs and their corresponding outputs in a logical statement. It is important in science because it helps us to determine the validity and consistency of a logical argument or statement.

## 2. How do you construct a truth table with 1 and 0?

To construct a truth table with 1 and 0, first list out all possible combinations of inputs. Then, for each input combination, determine the output based on the logical operators (AND, OR, NOT) being used. The output will be represented as either 1 (true) or 0 (false) in the truth table.

## 3. What are some common logical operators used in truth tables?

Some common logical operators used in truth tables include AND (represented as • or &), OR (represented as + or ||), and NOT (represented as ~ or !). These operators help to determine the overall output based on the input combinations.

## 4. How can truth tables be used to test the validity of an argument?

Truth tables can be used to test the validity of an argument by representing the premises and conclusion of the argument as logical statements. The truth table will then show all possible combinations of inputs and their corresponding outputs, allowing us to determine if the argument is valid or not.

## 5. Are there any limitations to using truth tables in science?

Yes, there are limitations to using truth tables in science. Truth tables can only be used for simple logical statements and cannot account for complex real-world situations. Additionally, they do not take into account probability or uncertainty, which are important factors in scientific research.

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