# help with boolean expressions and truth table

#### fishguts

Joined Sep 3, 2007
22
I need to make a truth table for the following equation, but I have no idea where to start I have not seen an equation like this before

F=(A+!B+C)(A+!C)(B+!C)

I was also wondering if I simplified this equation correctly

#### thingmaker3

Joined May 16, 2005
5,083
To create your truth table, make one column for A, one for B, one for C, and one for F.

Fill in the first three columns with the eight possible combinations. Apply the equation to each row to determine if F is true or false for that row. Tedious, yes, but not difficult. #### fishguts

Joined Sep 3, 2007
22
Alright so for

F=(A+!B+C)(A+!C)(B+!C)

I just make a truth table liek any other equation? There is not anything special to do since it contains ()?

#### Papabravo

Joined Feb 24, 2006
20,133
You do know that the three expressions in parentheses are to be AND'ed together -- don't you? In the algebra of real numbers the implied operation would be multiplication.

#### thingmaker3

Joined May 16, 2005
5,083
No matter how the equation is re-phrased, there are still only three variables. That means three input columns in the table. All truth tables work the same way. Doing the algebra first would, of course, make table generation easier.

#### techroomt

Joined May 19, 2004
198
if you convert your maxterm equation to a minterm, truth table generation is much simpler.

#### Karandeep Singh

Joined Oct 30, 2007
6
iam not sure

but method to decode can be by using de morgan theorem
(A+!B+C)(A+!C)(B+!C)
BY DE MORGAN
AND SOLVING I GET
B(A.{C BAR}+C)

#### agentofdarkness

Joined Oct 9, 2007
42

#### Papabravo

Joined Feb 24, 2006
20,133
Exclamation point "!" is a commonly use symbol for "NOT" or "Complement"

So if A=0 then !A=1 and vice versa

#### agentofdarkness

Joined Oct 9, 2007
42
I think the easiest way to generate a truth table is to first write down all the combinations of A,B,C (000-111). Then fill in the maxterms. A max term is combination of variables that will give you a result of logic 0. For this equation, 2 (ABC=010) is a maxterm. For all the blank spaces you get after you fill in the maxterms, fill in 1s. The maxterms will be
2(010)
1(001)
3(011)
1(001)
5(101)

Fill all the other rows with 1s. This form is known as Product of Sums. You have probably already solved the problem but hopefully some other people will find it helpful. I know that when I was first learning this stuff I had problems with it as well.