# Logic AND Function

In 1854, George Boole performed an investigation into the “laws of thought” which were based around a simplified version of the “group” or “set” theory, and from this Boolean Algebra was developed.

Boolean Algebra deals mainly with the theory that both logic and set operations are either “TRUE” or “FALSE” but not both at the same time.

For example, A + A = A and not 2A as it would be in normal algebra. Boolean Algebra is a simple and effective way of representing the switching action of standard Logic Gates and the basic logic statements which concern us here are given by the logic gate operations of the AND, the OR and the NOT gate functions.

## The logic AND Function

The Logic AND Function function states that two or more events must occur together and at the same time for an output action to occur. The order in which these actions occur is unimportant as it does not affect the final result. For example, A & B = B & A. In Boolean algebra the Logic AND Function follows the Commutative Law which allows a change in position of either variable.

The AND function is represented in electronics by the dot or full stop symbol ( . ) Thus a 2-input (A B) AND Gate has an output term represented by the Boolean expression A.B or just AB.

Switch Representation of the AND Function

Here the two switches, A and B are connected together to form a series circuit. Therefore, in the circuit above, both switch A AND switch B must be closed (Logic “1”) in order to put the lamp on. In other words, both switches must be closed, or at logic “1” for the lamp to be “ON”.

Then this type of logic gate ( an AND Gate ) only produces an output when “ALL” of its inputs are present. In Boolean Algebra terms the output will be TRUE only when all of its inputs are TRUE. In electrical terms, the logic AND function is equal to a series circuit as shown above.

As there are only two Switches, each with two possible states “open” or “closed”. Defining a Logic “0” as being when the switch is open and a Logic “1” when the switch is closed, there are then four different ways or combinations of arranging the two switches together as shown.

AND Function Truth Table
 Switch A Switch B Output Description 0 0 0 A and B are both open, lamp OFF 0 1 0 A is open and B is closed, lamp OFF 1 0 0 A is closed and B is open, lamp OFF 1 1 1 A is closed and B is closed, lamp ON Boolean Expression (A AND B) A . B

Logic AND gates are available as standard i.c. packages such as the common TTL 74LS08 Quadruple 2-input Positive AND Gates, (or the 4081 CMOS equivalent) the TTL 74LS11 Triple 3-input Positive AND Gates or the 74LS21 Dual 4-input Positive AND Gates. AND Gates can also be “cascaded” together to produce circuits with more than just 4 inputs.

• M
Mohd. Kaunain Raza

I just put it the AND Gate and OR Gate in parallel and in series NOT Gate . the result is not match to any gate . The truth table is very different and interesting , may you help me for making this circuit by sending me the circuit diagram . I have already send you the site which is just little different to my design . Convert it into my design which I already tell you and help me . May it will use full or not just tell me . THANKYOU.

• Z
Zeeshan ali

• d
dominicko

well,i would like to suggest that just add a function

• a
anteneh

hello sir how are you im a new student i want to get it an a bolean algebra and linear algebra and all mathematics parts so do you have application please send me thank you for your collaboration……..

• S
SathyaS

Hai… sir i am a new student … I want some more information about AND gates… Its very urgent sir.. And also send me the application of that gate…

• L
Lokesh babu chintha

Nothing

• m

i need the answer for these questions
1.reduce AB+(AC)’+AB’C(AB+C) by using boolean expression
2. prove that ABC+ABC’+AB’C+A’BC=AB+AC+BC

• v
vikramsinh doke

sir i want the cicruit using diode and transistor for the boolean expression AB+CD plzz help mi

• s
salisu baba dukawa kano

thank alout sir,for a very helful,educative tutorial.i always going through lesson what made me diffirent with other leaner.

• R
Ramesh

Any body known as an electronic implementation ?

Looking for the latest from TI?