## Nand Gate Truth Table

Contents

- 1 Which is NAND gate?
- 2 Is NAND a Boolean function?
- 3 Is NAND gate universal?
- 4 Do computers use NAND gates?
- 5 Is NAND an operator?
- 6 How many transistors are in a NAND gate?
- 7 What is NAND and NOR logic gates?
- 8 What is the logic function of NAND gate?

### What is the truth table for NAND gate?

NAND Gate Truth Table. The output of the NAND gate is always at logic high/’1″ and only goes to logic low/’0″ when all the inputs to the NAND gate are at logic 1. In other words, we can say that the output of the NAND gate always continues true if at least one of its inputs remains false or logic low.

#### Is NAND the same as XOR?

What are XOR and NAND? – XOR and NAND are two of the basic logical operators that can be used to create Boolean expressions. XOR stands for exclusive OR, and it means that one and only one of the operands must be true for the expression to be true. For example, A XOR B is true if A is true and B is false, or vice versa, but not if both are true or both are false.

### How to read NAND gate?

Logic NAND Gate Equivalence The Boolean expression for a logic NAND gate is denoted by a single dot or full stop symbol, (.) with a line or Overline, ( ‾‾ ) over the expression to signify the NOT or logical negation of the NAND gate giving us the Boolean expression of: A.B = Q.

#### Is NAND a gate or logic?

Hint: When we join the inputs of a NAND gate we can obtain a NOT gate. Also, when joining the two inputs of a NOR gate together we can obtain a NOT gate. Formula used: In this solution we will be using the following formula; \ where \ is an input. \, \ signifies the OR gates acting on input A and B, \, AND signifies the AND gates acting on input A and B Complete answer: To obtain an AND gate from NAND gates, we first feed the inputs A and B into the NAND gates. To obtain OR gate from NAND gates, we feed input A into a NAND with the input joined together to obtain a NOT (A), we feed input B into another NAND gate NAND with the input joined together to obtain NOT (B). Now the NOT (A) and NOT (B) are fed into separate input of another NAND gate. Hence, it becomes a NAND(NOT(A) NOT (B)) or \ which is equal to the OR gate. Boolean formula: \

A | B | \ | \ | \ |

1 | 1 | |||

1 | 1 | 1 | ||

1 | 1 | 1 | ||

1 | 1 | 1 |

To obtain an OR gate from NOR gates, the input A and B is fed into a NOR gate (into the separate inputs), then the output say Y which is NOT(A or B) is fed into two another NOR gates with the inputs combined to have a NOT (NOR Y) which is an OR gate. Boolean formula: \ To obtain an AND gate from NOR gates, we feed input A and B into two separate NOR gates with joined input to obtain a NOT (A) and a NOT (B) separately. Then this two different outputs are fed into either input (i.e. NOT (A) to one Input terminal and NOT (B) to another terminal). The result will be an AND gate. Boolean formula: \

A | B | \ | \ | Z |

1 | 1 | |||

1 | 1 | |||

1 | 1 | |||

1 | 1 | 1 |

img class=’aligncenter wp-image-189362 size-full’ src=’https://www.saradaschool.in/wp-content/uploads/2023/09/gemydiresupi.png’ alt=’Nand Gate Truth Table’ /> Note: For clarity, joining the inputs of NAND and NOR gate gives us NOT gate because AND and OR act necessarily on two inputs. Hence, when the inputs NAND (or NOR) are joined to allow only one input, it opens the AND (or OR) circuit and acts as NOT circuit, since NAND actually means NOT-AND and NOR means NOT-OR. So when the AND and NOR are removed it becomes a NOT.

### What is NAND gate formula?

From Wikipedia, the free encyclopedia

NAND gate truth table | ||
---|---|---|

Input | Output | |

A | B | A NAND B |

1 | ||

1 | 1 | |

1 | 1 | |

1 | 1 | 0 |

MIL/ANSI Symbol IEC Symbol DIN Symbol In digital electronics, a NAND gate ( NOT-AND ) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate, A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results.

A NAND gate is made using transistors and junction diodes. By De Morgan’s laws, a two-input NAND gate’s logic may be expressed as A • B = A + B, making a NAND gate equivalent to inverters followed by an OR gate, The NAND gate is significant because any boolean function can be implemented by using a combination of NAND gates.

This property is called functional completeness, It shares this property with the NOR gate, Digital systems employing certain logic circuits take advantage of NAND’s functional completeness. NAND gates with two or more inputs are available as integrated circuits in transistor-transistor logic, CMOS, and other logic families,

## Which is NAND gate?

What is a NAND gate? – The NAND gate or “NotAND” gate is the combination of two basic logic gates, the AND gate and the NOT gate connected in series. The NAND gate and NOR gate can be called the universal gates since the combination of these gates can be used to accomplish any of the basic operations.

- Hence, NAND gate and NOR gate combination can produce an inverter, an OR gate or an AND gate.
- The output of a NAND gate is high when either of the inputs is high or if both the inputs are low.
- In other words, the output is always high and goes low only when both the inputs are high.
- The logic NAND function is given by the Boolean expression \(\begin Y=\bar \end \),

Here A, B are the inputs and Y is the output. The Boolean expression given for a NAND gate is that of logical addition and it is opposite to AND gate. The Boolean expression is given by a single dot (.) with an overline over the expression to show the NOT or the logical negation of the NAND gate.

#### Why is NAND gate universal?

Thus, the NAND gate is a universal gate since it can implement the AND, OR and NOT functions. NAND Gate is a Universal Gate: To prove that any Boolean function can be implemented using only NOR gates, we will show that the AND, OR, and NOT operations can be performed using only these gates.

#### What does NAND stand for?

What does NAND stand for? – NAND stands for “NOT AND,” which refers to the Boolean operator or logic gate that governs the internal circuit of a NAND cell. The NAND operator produces a FALSE value only if both inputs are TRUE.

## Is NAND a Boolean function?

Thus implementing other Boolean functions purely out of NAND gates became a design goal. This is possible because, all by itself, the NAND gate is a complete Boolean basis.

#### What is the rule of NAND?

Rule for a NAND gate: output is not ‘high’ if both the first input and the second input are ‘high.’ Rule for a NOR gate: output is not ‘high’ if either the first input or the second input are ‘high.’ A Negative-AND gate behaves like a NOR gate. A Negative-OR gate behaves like a NAND gate.

#### What is NAND logic gate?

Definition – NAND is an abbreviation for “NOT AND.” A two-input NAND gate is a digital combination logic circuit that performs the logical inverse of an AND gate. While an AND gate outputs a logical “1” only if both inputs are logical “1,” a NAND gate outputs a logical “0” for this same combination of inputs. Figure 1. Symbol and truth table for NAND gate

#### Why is NAND gate called negative-OR gate?

➢ A NAND gate can be used for an OR operation that requires one or more LOW inputs to produce a HIGH output. ➢ This aspect of NAND operation is referred to as negative-OR. The term negative in this context means that the inputs are defined to be in the active or asserted state when LOW.

## Is NAND gate universal?

The NAND gate and NOR gate are called Universal gates because they can perform all the three essential functions of AND, OR and NOT gates. A two-input NAND gate is a digital combination logic circuit that performs the logical inverse of an AND gate.

## Do computers use NAND gates?

Computers also use other logic gates like NAND, NOR, and XOR. Each logic gate operates on inputs in a slightly different way; they output 1 and 0 in different situations.

## Is NAND an operator?

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld NAND, also known as the Sheffer stroke, is a connective in logic equivalent to the composition NOT AND that yields true if any condition is false, and false if all conditions are true, NAND is equivalent to, where denotes NOT and denotes AND, In propositional calculus, the term alternative denial is used to refer to the NAND connective. Notations for NAND include and (Mendelson 1997, p.26). The NAND operation is implemented as Nand, The circuit diagram symbol for an NAND gate is illustrated above. The binary NAND operator has the following truth table (Mendelson 1997, p.27). The NAND operation is the basic logical operation performed by the solid-state transistors (“NAND gates”) that underlie virtually all integrated circuits and modern computers. can be written in terms of NANDs as

#### How to use NAND gate?

Procedure for Conversion – Consider the following circuit. We have: We have to somehow re-implement this circuit using only NAND gates. Suppose what happens if we insert two inverters between each AND gate and OR gate. This circuit is completely equivalent to the original one as the output of each AND gate is being complemented twice before the signal reaches the OR gate. These inverters will play a key role in the process of conversion. Now take a look at the highlighted areas. The gates in each highlighted area can be easily combined into one NAND gate since it is basically just an AND gate followed by an inverter. We get: Now we only have to take care of the blue highlighted area. Recall the implementation of a NAND operation using OR & inverter gates we have covered above, the gates in the blue area implement a NAND operation. Therefore we can just replace all the gates in the blue area with a single NAND gate! Our Final Result: You can verify for yourself that this circuit implements the function AB + CD, same as that of the original circuit. Another Example: Original Circuit: (A+B + CD)E Method 1 First, we start by replacing the first AND gate(highlighted yellow) with a NAND gate. To do this we insert two inverters after this AND gate. Remember that this circuit is the same as two complement operations resulting in the original signal. The AND gate and the inverter that follows it can be combined into a single NAND gate(see yellow highlighted area). Next, we replace the OR gate in the blue highlighted area with NAND gates. We have seen how to implement OR operation using NAND gates, we put that knowledge to use now. We then proceed to replace the last AND gate(highlighted yellow) with NAND gates. Just like we replaced the OR gate in the previous step, we replace the AND gate with its equivalent NAND gate circuit. We now are left with an OR Gate and an Inverter Gate. A NAND gate can be implemented by an OR gate with complemented inputs. Here we have only one complemented input to the OR gate. To meet the condition that both the inputs are complemented, we insert two inverters between the highlighted OR gate and the preceding NAND gate. We get: Now both the inputs to the OR gate are complemented. The gates in the blue area represent a NAND operation so we can replace them with a NAND gate. We are now only left with an Inverter. An Inverter gate is basically a one-input NAND gate. We make the necessary replacement and obtain our final circuit. Our Final NAND gate-only circuit: You can verify that this circuit implements : (A+B + CD)E Method 2 (SOP Method): The original circuit implements the boolean function : (A+B+CD)E We first manipulate this boolean equation so that it is in the Sum of Products(SOP). In this case, we simply multiply each term in the parenthesis by E. Just like in example 1, we insert two inverter gates between each AND gate and OR gate. You can probably now figure out what we will do next. We combine the gates in the Yellow areas into one single NAND gate. Also, we know that an OR gate with complemented inputs implements a NAND operation. So we replace the gates in the blue area with a NAND gate. Our final circuit: We can conclude that whenever a circuit has a series of AND gates at the first level followed by a single OR gate, we can blindly replace each gate with a NAND gate and the circuit will still implement the same boolean function. In this case Method 2, took a lot less effort than Method 1, one might wonder why even bother learning Method 1 when Method 2 seems easier? The answer is that Method 2 requires that the boolean equation must be represented in Sum of Products form.

### Can NAND gate have one input?

What Is a NAND Gate? –

- A NAND gate is a two-input and single output device. The number of inputs can be two or more according to the need.
- A NAND gate means, it is a combinational logic circuit and a NAND gate is formed by combining an AND gate followed by a NOT gate.
- If any of the one input is 0 then the output will be 1. In other words, the NAND gate will give output as high logic if any one of the inputs among the two is 0.

## How many transistors are in a NAND gate?

One NAND gate has one transistor, as a result, three NAND gates will have three transistors.

#### Why is it called NAND?

NAND flash memory is named after the NAND logic gate. Since its introduction in the late 1980s, it has dominated the flash memory industry of SSDs and the electronics industries due to its highly dense storage and low cost.

#### What is NAND and XOR gate?

NAND, NOR, and XOR Logic Gates The definition of the OR operation is that it is TRUE if either input is TRUE. This includes the possibility that both inputs are TRUE. In contrast, the exclusive OR operation or XOR (sometimes called EOR) gate is TRUE if and only if a single input is true.

## What is NAND and NOR logic gates?

What is a NOR Gate? – The NOR gate is a combination of NOT and OR gates, i.e. OR + NOT = NOR, A NOR gate consists of an OR gate followed by a NOT gate. For the NOR gate, the output of the gate is high (1), when all its inputs are low (0). In all other cases, it produces a low output.

Thus, the NOR gate is nothing but a negated version of the OR gate. The Boolean expression of a two input NOR gate is given by, $$Y\:=\:\overline =\:\:(A\:+\:B)^\prime$$ Where, Y is the gate’s output and A & B are the inputs. Hence, from the Boolean expression of the NOR gate, it is clear that the gate’s output can be obtained by the logical addition of all the inputs and then taking the complement of the result of addition.

The following is the truth table of a two input NOR gate −

Inputs | OR | Output | |
---|---|---|---|

A | B | A+B | Y = (A+B)’ |

1 | |||

1 | 1 | ||

1 | 1 | ||

1 | 1 | 1 |

The NOR gate is used in the realization of several combinational and sequential digital circuits like multiplexers, multipliers, counters, etc. NAND and NOR gates are types of universal logic gates, however, there are several differences between these that are listed in the following table-

Basis of Difference | NAND Gate | NOR Gate |
---|---|---|

Definition | A NAND gate is a universal logic gate which performs the negated logical multiplication. | A NOR gate is a universal logic gate which performs the negated logical addition. |

Implementation | NAND gate can be implemented by using an AND gate followed by a NOT gate. | NOR gate can be implemented by using an OR gate followed by a NOT gate. |

Representation | The operation of NAND gate can be represented by the complimented AND operation, i.e.(.)’. | The operation of a NOR gate can be represented by the complimented OR operation, i.e. (+)’. |

Boolean expression | The Boolean expression of a two input NAND gate is given by, $$Y\:=\:\overline =\:\:(A\:\cdot\:B)^\prime$$ | The Boolean expression of a two input NOR gate is given by, $$Y\:=\:\overline =\:\:(A\:+\:B)^\prime$$ |

Low output | The NAND gate produces a low (0) output, when all its inputs are high. | The NOR gate produces a low (0) output, when all its inputs or at least one input is high (1). |

High output | The NAND gate produces a high (1) output, when all its inputs or at least one input is low (0). | The NOR gate produces a high (1) output, when all its inputs are low (0). |

Applications | The NAND gate is used in constructing other logic gates, making flip-flops, registers, implementing burglar alarm circuit, freezer warning buzzer, etc. | The NOR gate is used in the implementation of various combinational and sequential digital circuits like multiplexers, multipliers, counters, etc. |

#### What is the logic of a NAND 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.

#### How do you solve NAND gates?

Procedure for Conversion – Consider the following circuit. We have: We have to somehow re-implement this circuit using only NAND gates. Suppose what happens if we insert two inverters between each AND gate and OR gate. This circuit is completely equivalent to the original one as the output of each AND gate is being complemented twice before the signal reaches the OR gate. These inverters will play a key role in the process of conversion. Now take a look at the highlighted areas. The gates in each highlighted area can be easily combined into one NAND gate since it is basically just an AND gate followed by an inverter. We get: Now we only have to take care of the blue highlighted area. Recall the implementation of a NAND operation using OR & inverter gates we have covered above, the gates in the blue area implement a NAND operation. Therefore we can just replace all the gates in the blue area with a single NAND gate! Our Final Result: You can verify for yourself that this circuit implements the function AB + CD, same as that of the original circuit. Another Example: Original Circuit: (A+B + CD)E Method 1 First, we start by replacing the first AND gate(highlighted yellow) with a NAND gate. To do this we insert two inverters after this AND gate. Remember that this circuit is the same as two complement operations resulting in the original signal. The AND gate and the inverter that follows it can be combined into a single NAND gate(see yellow highlighted area). Next, we replace the OR gate in the blue highlighted area with NAND gates. We have seen how to implement OR operation using NAND gates, we put that knowledge to use now. We then proceed to replace the last AND gate(highlighted yellow) with NAND gates. Just like we replaced the OR gate in the previous step, we replace the AND gate with its equivalent NAND gate circuit. We now are left with an OR Gate and an Inverter Gate. A NAND gate can be implemented by an OR gate with complemented inputs. Here we have only one complemented input to the OR gate. To meet the condition that both the inputs are complemented, we insert two inverters between the highlighted OR gate and the preceding NAND gate. We get: Now both the inputs to the OR gate are complemented. The gates in the blue area represent a NAND operation so we can replace them with a NAND gate. We are now only left with an Inverter. An Inverter gate is basically a one-input NAND gate. We make the necessary replacement and obtain our final circuit. Our Final NAND gate-only circuit: You can verify that this circuit implements : (A+B + CD)E Method 2 (SOP Method): The original circuit implements the boolean function : (A+B+CD)E We first manipulate this boolean equation so that it is in the Sum of Products(SOP). In this case, we simply multiply each term in the parenthesis by E. Just like in example 1, we insert two inverter gates between each AND gate and OR gate. You can probably now figure out what we will do next. We combine the gates in the Yellow areas into one single NAND gate. Also, we know that an OR gate with complemented inputs implements a NAND operation. So we replace the gates in the blue area with a NAND gate. Our final circuit: We can conclude that whenever a circuit has a series of AND gates at the first level followed by a single OR gate, we can blindly replace each gate with a NAND gate and the circuit will still implement the same boolean function. In this case Method 2, took a lot less effort than Method 1, one might wonder why even bother learning Method 1 when Method 2 seems easier? The answer is that Method 2 requires that the boolean equation must be represented in Sum of Products form.

## What is the logic function of NAND gate?

Logical functions are used in spreadsheets to test whether a situation is true or false. Depending on the result of that test, you can then elect to do one thing or another. These decisions can be used to display information, perform different calculations, or to perform further tests.

### What are the basic gates by NAND?

2)Nor gate as Universal Gate – NOR gate is actually a combination of two logic gates: OR gate followed by NOT gate. So its output is complement of the output of an OR gate.This gate can have minimum two inputs, output is always one. By using only NOR gates, we can realize all logic functions: AND, OR, NOT, Ex-OR, Ex-NOR, NAND. So this gate is also called universal gate.