# How is the truth table of 3 input Logic Gates derived?

#### Devika B S

Joined Mar 8, 2017
144
I am not able to understand the logic behind the truth tables of 3 input gates. For example, consider the input: 1 0 0
Output of this is 1 as per the truth table.
But isn't it 1.(0.0) = 1.0 = 0 ? Am I not allowed to use Boolean algebra in this manner?

( I have this intuition that there is a terrible blunder being committed somewhere, but I am not very sure of the concepts involved in truth tables)

#### MrChips

Joined Oct 2, 2009
21,041
Can you post an link or reference to the truth table in question?
There is either an error or a misunderstanding.

#### Devika B S

Joined Mar 8, 2017
144
Can you post an link or reference to the truth table in question?
There is either an error or a misunderstanding. #### MrChips

Joined Oct 2, 2009
21,041
That is a mistake.

Only the last line A=1, B=1, C=1 gives Output =1 for A.B.C.

• Devika B S

#### Devika B S

Joined Mar 8, 2017
144
Can you post an link or reference to the truth table in question?
There is either an error or a misunderstanding. But another truth table for AND gate online is this. So I guess the first truth table is not that of AND gate? I am not having 3 input gates in my textbook. I am looking at materials online.

#### Devika B S

Joined Mar 8, 2017
144
That is a mistake.

Only the last line A=1, B=1, C=1 gives Output =1 for A.B.C.
OK Thank you for the clarification.

#### Papabravo

Joined Feb 24, 2006
13,688
Other properties of the AND (&) function is that it is commutative and associative.
1. A&B = B&A -- Commutative Property
2. (A&B)&C = A&(B&C) -- Associative Property
The gates work the same way as the algebra.

• Devika B S