I am trying to constuct a truth table from Z=(A+(not)B).(B+C).((not)A+B+D)?

In summary, a truth table is a table used in logic to show all possible combinations of inputs and their corresponding outputs for a logical expression. To construct a truth table, list all the variables or inputs, create columns for each variable and an additional output column, fill in the columns with all possible combinations of inputs, use logical operators to determine the output, and label the output column with the logical expression. The logical expression for Z=(A+(not)B).(B+C).((not)A+B+D) is simply Z because it is already in its most simplified form. The truth table for this expression will have 16 rows. To determine the validity of a logical statement, look at the output column of the truth table and consider
  • #1
mm391
66
0

Homework Statement



Construct a truth table to show:

Z=(A+(not)B).(B+C).((not)A+B+D)

Homework Equations


The Attempt at a Solution



from 0,0,0,0 to 1,1,1,1 i get

0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1
 
Last edited:
Physics news on Phys.org
  • #2
Hi mm391! Is there a question that was intended to accompany your post here?
 
  • #3
Ok
0,0,1,1,0,0,0,0,0,0,0,1,1,1,1,1
 

1. What is a truth table?

A truth table is a table used in logic to show all possible combinations of inputs and their corresponding outputs for a logical expression. It is a helpful tool for evaluating the validity of logical statements.

2. How do I construct a truth table?

To construct a truth table, you must first list all the variables or inputs for the logical expression. Then, you will create columns for each variable and an additional column for the output. Next, fill in the columns with all possible combinations of inputs and use the logical operators (such as AND, OR, NOT) to determine the output for each combination. Finally, label the output column with the logical expression and write "true" or "false" for each output.

3. What is the logical expression for Z=(A+(not)B).(B+C).((not)A+B+D)?

The logical expression for Z=(A+(not)B).(B+C).((not)A+B+D) is simply Z. This is because the logical expression is already in its most simplified form, and Z represents the output of the expression.

4. How many rows will my truth table have for this expression?

This truth table will have 16 rows. This is because there are 4 variables (A, B, C, D) and each variable has 2 possible values (true or false), resulting in 2^4 = 16 possible combinations of inputs.

5. How do I use a truth table to determine the validity of a logical statement?

To determine the validity of a logical statement, you can look at the output column of the truth table. If the output is always true for every combination of inputs, then the statement is considered logically valid. If there is at least one combination of inputs that results in a false output, then the statement is considered invalid.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
15
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
1K
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
14
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
Replies
2
Views
929
  • Engineering and Comp Sci Homework Help
Replies
20
Views
2K
Back
Top