And Gate Truth Table
Contents
- 1 Why is it called an AND gate?
- 2 What is an example of an AND gate?
- 3 How do you make an AND gate?
- 4 What is the formula for the AND gate?
- 5 Who invented logic gates?
- 6 Can an AND gate have 3 inputs?
- 7 What are the 3 types of logic gates?
What is an AND gate truth table?
AND Gate Truth Table – The AND gate truth table is for the two fan-in or inputs, A and B. It has only one output as Y. The output is logic ‘0’ if any inputs A and B are LOW (logic ‘0’). However, the output is 1 only when all the inputs are 1. The AND gate truth table is as follows: The logical expression from the above AND gate truth table is Y= AB.
What does a AND gate do?
| Input A | Input B | Output |
|---|---|---|
| false | false | false |
| false | true | false |
| true | false | false |
| true | true | true |
An AND gate is a digital logic gate with two or more inputs and one output that performs logical conjunction, The output of an AND gate is true only when all of the inputs are true, If one or more of an AND gate’s inputs are false, then the output of the AND gate is false, The truth table for an AND gate with two inputs appears to the right.
What is the truth table for an AND gate with two inputs?
The 2-input Logic AND Gate –
| Symbol | Truth Table | ||
| 2-input AND Gate | B | A | Q |
| 1 | |||
| 1 | |||
| 1 | 1 | 1 | |
| Boolean Expression Q = A.B | Read as A AND B gives Q |
What is a NAND gate AND gate truth table?
A NAND gate with two inputs is a digital combination logic circuit that performs the logical inverse of an AND gate. In the NAND Gate truth table, while an AND gate only outputs a logical ‘1’ if both inputs are logical ‘1,’ a NAND gate outputs a logical ‘0’ for the same input combination.
Why is it called an AND gate?
Basic logic gates – There are seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR, and XNOR. AND | OR | XOR | NOT | NAND | NOR | XNOR The AND gate is so named because, if 0 is called “false” and 1 is called “true,” the gate acts in the same way as the logical “and” operator. AND gate
| Input 1 | Input 2 | Output |
| 1 | ||
| 1 | ||
| 1 | 1 | 1 |
The OR gate gets its name from the fact that it behaves after the fashion of the logical inclusive “or.” The output is “true” if either or both of the inputs are “true.” If both inputs are “false,” then the output is “false.” In other words, for the output to be 1, at least input one OR two must be 1. OR gate
| Input 1 | Input 2 | Output |
| 1 | 1 | |
| 1 | 1 | |
| 1 | 1 | 1 |
The XOR ( exclusive-OR ) gate acts in the same way as the logical “either/or.” The output is “true” if either, but not both, of the inputs are “true.” The output is “false” if both inputs are “false” or if both inputs are “true.” Another way of looking at this circuit is to observe that the output is 1 if the inputs are different, but 0 if the inputs are the same. XOR gate
| Input 1 | Input 2 | Output |
| 1 | 1 | |
| 1 | 1 | |
| 1 | 1 |
A logical inverter, sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. It reverses the logic state. If the input is 1, then the output is 0. If the input is 0, then the output is 1. Inverter or NOT gate The NAND gate operates as an AND gate followed by a NOT gate. It acts in the manner of the logical operation “and” followed by negation. The output is “false” if both inputs are “true.” Otherwise, the output is “true.” NAND gate
| Input 1 | Input 2 | Output |
| 1 | ||
| 1 | 1 | |
| 1 | 1 | |
| 1 | 1 |
The NOR gate is a combination OR gate followed by an inverter. Its output is “true” if both inputs are “false.” Otherwise, the output is “false.” NOR gate
| Input 1 | Input 2 | Output |
| 1 | ||
| 1 | ||
| 1 | ||
| 1 | 1 |
The XNOR (exclusive-NOR) gate is a combination XOR gate followed by an inverter. Its output is “true” if the inputs are the same, and “false” if the inputs are different. XNOR gate
| Input 1 | Input 2 | Output |
| 1 | ||
| 1 | ||
| 1 | ||
| 1 | 1 | 1 |
Complex operations can be performed using combinations of these logic gates. In theory, there is no limit to the number of gates that can be arrayed together in a single device. But in practice, there is a limit to the number of gates that can be packed into a given physical space.
What is an example of an AND gate?
Introduction: AND Gate for Logic Circuit Applications – Logic gates are the fundamental building blocks of digital circuits; it’s how computers record and transmit information! The most basic logic gates (like the AND gate) help you interpret two binary inputs to control a single output.
Binary means that the inputs leading into the gate have two possible states like “on or off.” Some examples would be two switches that are either “open or closed;” two light sensors that are either “bright or dark;” or two temperature sensors that are “hot or cold.” The single output might be an LED that is either “on or off.” In the case of the AND gate, if both inputs are ON then the output is also ON.
Any other combination of inputs results in the output being OFF. The truth table shown above helps to illustrate this pattern. The venn diagram next to it is another way to visualize the AND gate. The area of overlap between A and B is highlighted because the only way to make the output turn ON is when inputs A and B are both ON.
- An example of an AND gate project would be a gumball machine.
- Input A: Coin inserted or not inserted Input B: Button pushed or not pushed Output: Gumball dispensed or not dispensed In order to dispense a gumball, you have to insert a coin AND press the button! In this Instructable you will learn how to create your own AND gate with Circuit Scribe ink, transistors, and resistors.
Materials
Circuit Scribe conductive ink pen Sheet of paper (preferably photo paper) Metal Sheet Circuit Stencil 9V battery and adapter module 2x NPN Transistor modules Bi-Directional LED module 2x SPST Switch modules 3x 2-Pin modules 2x 10 k-ohm resistors 1x 5 k-ohm resistors
These materials were purchased on the Autodesk 123D Circuits website,
What is an AND gate equivalent to?
An AND gate is equivalent to an inverted-input NOR gate. II. An OR gate is equivalent to an inverted-input NAND gate.
What are the rules of an AND gate?
An AND gate operates on logical multiplication rules. In this gate, if either of the inputs is low (0), then the output is also low. If all of the inputs are high (1), then the output will also be high. An AND gate can have any number of inputs, although 2 input and 3 input AND gates are the most common.
Can an AND gate have 3 inputs?
LogicBlocks Experiment Guide Contributors: jimblom 2 Sometimes you need to AND more than two inputs together. In fact, 3- and 4-input AND gates are just as common as the dual-input variety. Let’s make a 3-input AND gate out of two two-input AND gates.
What is negative AND gate?
The Negative-AND Gate A Negative-AND gate functions the same as an AND gate with all its inputs inverted (connected through NOT gates). In keeping with standard gate symbol convention, these inverted inputs are signified by bubbles.
What are the 2 basic logic gates?
All digital systems can be constructed by only three basic logic gates. These basic gates are called the AND gate, the OR gate, and the NOT gate. Some textbooks also include the NAND gate, the NOR gate and the EOR gate as the members of the family of basic logic gates. The description of the operations of these gates are listed below : The AND gate is a circuit which gives a high output (logic 1) if all its inputs are high. A dot ( ) is used to indicate the AND operation. In practice, however, the dot is usually omitted, The OR gate is a circuit which gives a high output if one or more of its inputs are high. A plus sign (+) is used to indicate the OR operation. The NOT gate is a circuit which produces at its output the negated (inverted) version of its input logic. The circuit is also known as an inverter, If the input variable is A, the inverted output is written as, The NAND gate is a NOT-AND circuit which is equivalent to an AND circuit followed by a NOT circuit. The output of the NAND gate is high if any of its inputs is low. The NOR gate is a NOT-OR circuit which is equivalent to an OR circuit followed by a NOT circuit. The output of the NOR gate is low if any of its inputs is high. EOR gate The Exclusive-OR gate is a circuit which gives a high output if either of its two inputs is high, but not both. A encircled plus sign ( ) is used to indicate the EOR operation.
| Copyright (C) 1998-99. HKIEd, All rights reserved. |
Is truth table a logic OR gate?
Thus the logic OR gate truth table can be correctly described as an ‘ Inclusive OR gate ‘ truth table because the output is true when both gate inputs are true (HIGH). Therefore, we can define the operation of a 2-input logic OR gate as: ‘If either A or B is true, then Q is true.’
What is the difference between AND AND NAND?
The NAND gate represents the complement of the AND operation. Its name is an abbreviation of NOT AND. The graphic symbol for the NAND gate consists of an AND symbol with a bubble on the output, denoting that a complement operation is performed on the output of the AND gate.
What is the symbol of AND gate?
It can also be denoted as symbol ‘^’ or ‘&’.
Can NAND gate have 3 inputs?
3 input NAND Gate Unlike the two-input NAND gate, the three-input NAND gate has three inputs. The symbolic representation of the three input NAND gate is as follows. The Boolean expression of the logic NAND gate is represented as the binary operation dot(.). Where A, B, and C are the inputs and Y is the output.
What is the difference between gate and AND gate?
Difference between AND Gate and OR Gate: –
| S.NO. | Parameter | AND Gate | OR Gate |
|---|---|---|---|
| 1. | Executes | AND Gate executes logical multiplication. | OR Gate executes logical addition. |
| 2. | Implements | AND Gate implements logical conjunction. | OR Gate implements logical disjunction. |
| 3. | Represent | AND Gate is represented by a dot(.) Example :- Z = A.B | OR Gate is represented by a plus(+). Example :- Z = A+B |
| 4. | True Output | AND Gate gives true output only when both inputs are true. | OR Gate gives a true output when at least one output is true. |
| 5. | High output | The AND Gate gives high output only if all its inputs are high | The OR Gate gives output if one or more of its inputs is high. |
ul> Last Updated : 16 Jun, 2022 Like Article Save Article
: Difference Between AND Gate and OR Gate
Why is NAND called universal gate?
| The NAND gate and the NOR gate can be said to be universal gates since combinations of them can be used to accomplish any of the basic operations and can thus produce an inverter, an OR gate or an AND gate, The non-inverting gates do not have this versatility since they can’t produce an invert. |
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Basic Gates
How do you make an AND gate?
Using Transistors to Build Bigger Circuits – Using transistors as building blocks, we can build larger circuits that perform interesting (logical) operations. Our first example is the NOT circuit. The figure below shows how to connect two transistors together to build an inverter (also known as a NOT gate). Figure 5: An inverter circuit (known as the NOT gate). Now, let’s find out what the inverter circuit above will do when presented with an input (i.e. X ). We know that X can take one of two values, either 0 or 1, Let’s study each one separately.
- If X=0 then by definition of the bottom transistor, it will be OFF, which means that electricity will not be able to flow from its source to its sink. Also, by definition, the top transistor will be ON, which means that electricity will be able to flow from its source to its sink. The question is, will there be any electricity coming out from Z (where Z is the output of that circuit). The answer is YES. Since the top transistor is ON and the bottom transistor is OFF, electricity flowing out of the battery will go through the top transistor but will not be able to make it through the bottom one. In other words, it will flow out through Z, To visualize the operation of the inverter, it may be helpful to think about this example using the water analogy discussed before.
- If X=1 then by definition of the bottom transistor, it will be ON, which means that any electricity already available at its source will drain in the sink. Also, by definition, the top transistor will be OFF, which means that no electricity will be able to flow from its source to its sink. The question is, will there be any electricity coming out from Z (where Z is the output of that circuit). The answer is NO. Since the top transistor is OFF and the bottom transistor is ON, electricity flowing out of the battery will be blocked by the top transistor and any electricity that may exist in Z, will drain. In other words, there will be no electricity flowing out through Z, Again, it may be helpful to think about this example using the water analogy discussed before.
The table below sums up the operation of the NOT gate by providing an output (Z) for every possible input (X) of the circuit. Tables like this one (providing us with the value of a function for all possible combination of inputs of that function) are called truth tables.
- Figure 6: Truth table summarizing operation of the inverter circuit (the NOT function).
The figure below shows how one could build another circuit using transistors. This circuit has two inputs X and Y and one output Z, Figure 7: The “not both X and Y” circuit (the NAND function). There are 4 possibilities for the inputs, namely
- X=0, Y=0
- X=0, Y=1
- X=1, Y=0
- X=1, Y=1
Let’s try to do an analysis similar to what we did for the NOT gate. In particular, consider the case when both X and Y are 0. By definition, the bottom two transistors will be OFF while the top two will be ON thus allowing electricity to flow from the battery to the output Z,
Thus for X=0, Y=0 we get Z=1, In the case when both X and Y are 1, the bottom two transistors will be ON while the top two will be OFF, thus no electricity will flow from the battery to the output Z, Thus for X=1, Y=1 we get Z=0, In the case when X=0 and Y=1, we notice that one of the two top transistors will be ON and the other will be OFF,
Similarly, for the bottom transistors, one will be ON and the other will be OFF, Thus, electricity will still be able to flow to Z (through the ON transistor on top), thus making Z=1, The case for X=1, Y=0 is similar. It yields Z=1, Thus we get the truth table below for the circuit shown above.
NAND
|
/td>
Figure 8: Truth table summarizing operation of the NAND gate. The above truth table says that the output of the circuit is 0 only when the two inputs are 1 this is exactly the opposite of the AND logical function (the AND logical function outputs 1 whenever both its first input AND its second input are 1).
Figure 9: The “both X and Y” circuit (the AND function). Similar to the NAND gate we can build a NOR (Not OR) gate as shown in the figure below. Figure 10: The “not X nor Y” circuit (the NOR function). We leave it as an exercise to check that the truth table for the above circuit is as shown below.
NOR
|
/td>
Figure 11: Truth table summarizing operation of the NOR gate. And, just as we were able to obtain the AND function by connecting the output of the NAND function to the input of the NOT function (see figure 9), we can obtain the OR function (which outputs 1 whenever at least one of its inputs is 1) by connecting the output of the NOR function to the input of the NOT function.
What is the formula for the AND gate?
Summary – A logic gate is one of the most basic switching circuits used in digital circuits to determine if an input pulse can pass through to the output. Logic gates are the building blocks of a digital circuit, and these perform various logical operations, which are necessary for any given digital circuit. Based on their operation, we have the following types of logic gates:
AND: The Boolean equation for AND gate is \(Y = A \cdot B\).OR: The Boolean expression for OR gate is: \(Y = A + B\).NOT: The Boolean expression for the NOT gate is: \(Y = \bar A\).NOR: The Boolean expression for the NOR gate is: \(Y = A + B\).NAND: The Boolean expression for the NAND gate is: \(Y = \overline \).XOR: the Boolean expression for the XOR gate is: \(Y = \bar A \cdot B + A \cdot \bar B\).XNOR: the Boolean expression for the XNOR gate is: \(Y = A \cdot B + \bar A\bar B\).
Is XNOR a universal gate?
Alternatives – XNOR gate circuit using three mixed gates If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. A circuit implementing an XNOR function can be trivially constructed from an XOR gate followed by a NOT gate. If we consider the expression ( A + B ¯ ) ⋅ ( A ¯ + B ) })\cdot ( }+B)}, we can construct an XNOR gate circuit directly using AND, OR and NOT gates. However, this approach requires five gates of three different kinds. As alternative, if different gates are available we can apply to transform ( A + B ¯ ) ⋅ ( A ¯ + B ) ≡ ( A ⋅ B ) + ( A ¯ ⋅ B ¯ ) })\cdot ( }+B)\equiv (A\cdot B)+( }\cdot })} as stated above, and apply to the last term to get ( A ⋅ B ) + ( A + B ) ¯ }} which can be implemented using only three gates as shown on the right. An XNOR gate circuit can be made from four NOR gates. In fact, both NAND and NOR gates are so-called “universal gates” and any logical function can be constructed from either or alone.
| Desired gate | NAND construction | NOR construction |
|---|---|---|
An alternative arrangement is of five NAND gates in a topology that emphasizes the construction of the function from ( A ⋅ B ) + ( A ¯ ⋅ B ¯ ) }\cdot })}, noting from that a NAND gate is an inverted-input OR gate. Another alternative arrangement is of five NOR gates in a topology that emphasizes the construction of the function from ( A + B ¯ ) ⋅ ( A ¯ + B ) })\cdot ( }+B)}, noting from that a NOR gate is an inverted-input AND gate.
| Desired gate | NAND construction | NOR construction |
|---|---|---|
For the NAND constructions, the lower arrangement offers the advantage of a shorter propagation delay (the time delay between an input changing and the output changing). For the NOR constructions, the upper arrangement requires fewer gates. From the opposite perspective, constructing other gates using only XNOR gates is possible though XNOR is not a fully,
Who invented logic gates?
George Boole Inventor of the idea of logic gates. He was born in Lincoln, England and he was the son of a shoemaker in a low class family.
Can an AND gate have 3 inputs?
LogicBlocks Experiment Guide Contributors: jimblom 2 Sometimes you need to AND more than two inputs together. In fact, 3- and 4-input AND gates are just as common as the dual-input variety. Let’s make a 3-input AND gate out of two two-input AND gates.
What are the 3 types of logic gates?
All digital systems can be constructed by only three basic logic gates. These basic gates are called the AND gate, the OR gate, and the NOT gate. Some textbooks also include the NAND gate, the NOR gate and the EOR gate as the members of the family of basic logic gates. The description of the operations of these gates are listed below : The AND gate is a circuit which gives a high output (logic 1) if all its inputs are high. A dot ( ) is used to indicate the AND operation. In practice, however, the dot is usually omitted, The OR gate is a circuit which gives a high output if one or more of its inputs are high. A plus sign (+) is used to indicate the OR operation. The NOT gate is a circuit which produces at its output the negated (inverted) version of its input logic. The circuit is also known as an inverter, If the input variable is A, the inverted output is written as, The NAND gate is a NOT-AND circuit which is equivalent to an AND circuit followed by a NOT circuit. The output of the NAND gate is high if any of its inputs is low. The NOR gate is a NOT-OR circuit which is equivalent to an OR circuit followed by a NOT circuit. The output of the NOR gate is low if any of its inputs is high. EOR gate The Exclusive-OR gate is a circuit which gives a high output if either of its two inputs is high, but not both. A encircled plus sign ( ) is used to indicate the EOR operation.
| Copyright (C) 1998-99. HKIEd, All rights reserved. |
What is a NOT gate with a truth table?
| Input | Output |
|---|---|
| false | true |
| true | false |
A NOT gate, often called an inverter, is a nice digital logic gate to start with because it has only a single input with simple behavior. A NOT gate performs logical negation on its input. In other words, if the input is true, then the output will be false, Similarly, a false input results in a true output. The truth table for a NOT gate appears to the right.
