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Logic AND Function

Logic AND Function

The Logic AND Function output is only true when all of its inputs are true, otherwise the output is false

Boolean Algebra is based around logical functions in which each Boolean function, such as the logic AND function, typically has one or more input values and produces an output result based on these input values. The inputs have one of two values: 0 or 1.

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

logic 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
 

2-input and function

 

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.

136 Comments

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  • Julio Barrientos

    Nice information

  • Kevin

    Great stuff. Thank you for the tutorials.

  • Dancun musembi

    Well described

  • Razia

    Perfect

  • Cheryl Chasakara

    A domestic heating system has a hot water tank and a number of radiators. There is a computerised management
    system which receives signals dependent on whether or not the conditions for components are as they should be.
    The following table summarises the signals received :
    Signal Value Component condition
    0 Wate r flow in the radiators is too low
    A
    1 Water flow in the rad iators is within limits
    0 Hot water tank temperature too high
    B
    1 Hot water tank temperature w ithi n limits
    0 Water level in hot water tank too low C
    1 Water level in hot water tank w ithin limits
    a Consider the following fault condition. The water level in the hot water tank is too low and the temperature
    in the hot water tank is too high. The management system must output a signal to switch off the system.
    Construct a tru th table for th is fault condition including the A, Band C signals.
    ii Construct the circuit diagram forth is fau lt co ndition to match this truth table.
    b Consider the fault co ndition where the hot water tank tem perature is with in limits but the water flow in the
    radiators is too low and the water level in the hot water t an k is too low. Construct the circuit diagram for this fault
    condition which requires the management system to output a signal to increase water pressure.

  • saradeen khan

    nyc

  • Daniel Mamjing Moses

    It’s very helpful

  • Brght

    I have really enjoyed the site

  • JUDE ONYEKACHI

    Please recommend a textbook on this for me

  • Funani

    I want to know boolean expression

  • Tikanand Dewoo

    I did a little of ladder logic, need to recap a bit. Would appreciate if PDF for this
    tutorial could be made available for download. thanks a lot.

  • Marcos hillary

    its a nice and accurate script

  • CHIJIOKE

    I need more information about ladder programming

  • Ummu

    Reading

  • Jaime Librado

    I was able to refresh about the AND Truth Table where the (Q) output state will be “high” if only all input states are all “high” as well.

  • Holaryhinkah

    Please I want to learn the logic gate

  • saba Khan

    Please help Kar da

  • Happiness

    Pls I want to learn this logic gate

  • Eng Maxamed Abdi xaashi

    Aad iyo aad ayaan ugu faraxsanahay casharadan waana sharro muhiim ah

  • Junior Fabian Kane

    We were asked to program a car remote, I did the diagram using gate simulator board on my computer, it’s an AND gate but the problem is written a code for every functions on the gate.