NAND Gate is created by applying NOT operation to an AND gate. Hence, the outputs of this gate are opposite to that of AND gate when the inputs are kept same. Shown below are the symbol and truth table for NAND gate.
Fig. 1 : Symbolic Representation Of NAND gate
Input 
 Output 
A  B  Y 
0  0  1 
0  1  1 
1  0  1 
1  1  0 
Basic logic gates consist of three basic logic gates namely NOT, AND and OR. Each of them performs a different logic function. We can derive logical function or any Boolean or logic expression by combination of these gate. Shown here are the logical method and the circuit through which one can obtain all the basic gates by only using NAND gates.
To understand the conversion we have to first understand the working of individual gates
1.NOT Gate This is the simplest form of a digital logic circuit . It is also called as inverter. It consists of only one input and one output. Input can only be binary number it may be one or zero. NOT gate is a logic element whose output stage is always the complement of the input stage means when you supply logic 1 we will logic 0 and vice versa. Now how many stage are possible is calculated by 2^{n} (where n is the number of input) means hear we have input equal to 1 so number of stage possible is 0 and 1 (2^{1}). Truth table of NOT gate is as follows
Input(2^{1}) 
Output 
A 
Y=NOT A 
0 
1 
1 
0 
2.AND Gate It is logic circuit has two input and one output. The operation of gate is such that output of gate is binary 1 if and only if all input are binary 1. If any of the input is binary 0 we will receive output as binary 0. Truth table of AND gate are as follows
Number of stage possible = 2^{n}
=2^{2} = 4
Input 
Output 

A 
B 
Y=A.B 
0 
0 
0 
0 
1 
0 
1 
0 
0 
1 
1 
1 
3.OR GateOr gate is another basic logic gate like AND gate it as two input and one output. The operation of gate is such that output of gate is binary 1 if any of the input is binary low and we will receive logic zero only when both the inputs are low. Truth table of OR gate are as follows
Number of stage possible = 2^{n}
=2^{2} = 4
Input 
Output 

A 
B 
Y=A+B 
0 
0 
0 
0 
1 
1 
1 
0 
1 
1 
1 
1 
4.NAND Gate The term NAND is a contraction of the expression NOT and AND gate. Therefore a NAND gate is an AND gate followed by the inverter. The operation of gate is such that output of gate is binary 1 if any of the input is binary low and we will receive logic zero only when both the inputs are high. Truth table and expression of NAND gate are as follows
Input 
Output 

A 
B 
Y=NOT(A AND B) 
0 
0 
1 
0 
1 
1 
1 
0 
1 
1 
1 
0 
For understanding this one should know about De Morganâ€™s theorem It states that complement of a product is equal to the sum of the complements.
We have used two NAND gate and short the input of each gate so we will get output as
= NOT (A) AND NOT (B)
Now it is again supplied to another NAND gate and we will get output as
= NOT (NOT (A) And NOT (B))
= [NOT (NOT) (A)]+ [NOT (NOT) (B)] (From EQ 1)
= A+ B
Circuit Diagrams
CircuitDiagramForConversionofNANDgatetoBasicgates  
CircuitDiagramConversionNANDgateBasicgates2 
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