NAND gate actually means “not AND gate” which means, the output of this gate is just reverse of that of a similar AND gate.
We know that the output of the AND gate is only high or 1, when all the inputs are high or 1. In all other cases, the output of AND gate is low or 0. In the case NAND, the case is a just opposite, here, the output is only low or 0 when and only when all inputs of the gate are 1 and in all other cases, the output of NAND gate is high or 1.
Hence, truth table of a NAND gate can be written like,
Just reverse of the truth table of AND gate which is
Like AND gate a NAND gate can also be more than two inputs, like 3, 4, input NAND gate.
An NAND gate is also referred as universal logic gate as all the binary operations can be realized by using only NAND gates.
There are three basic binary operations, AND, OR and NOT. By these three basic operations, one can realize all complex binary operations. Now, we will show all these three binary operations can be realized by using only NAND gates.
Realizing NOT Gate Using NAND GateWhen, both inputs of a two inputs NAND gate are zero, the output is 1 and both inputs of the NAND gate are 1, the output is 0. Hence a NOT gate can very easily be realized from NAND gate just by applying common inputs to the NAND gate. This is done by short circuiting all the inputs terminals of a NAND gate. Where, x is either 1 or 0.
Realizing AND Gate Using NAND GateAs we told earlier, a NAND gate is a NOT gate followed by an AND gate, so if we can cancel the effect of NOT gate in a NAND gate it will become an AND gate. Hence, a NOT gate followed by a NAND gate realizes an AND gate. In this case we use the NOT gate which is realized from NAND gate and the logic circuit is shown below,
Realizing OR Gate from NAND GateFrom De Morgan Theorem we know, The above equation is a logical OR operation. The above logic equation can be represented by gates as shown above, where inputs first inverted then passed through a third NAND gate.
The truth table of such circuit is, Now, we have proved that all three basic binary operations can be realized by using only NAND gates. Hence, any other simple or complex binary operation must also be realized by using only NAND gates and hence it is justified to call an NAND gates as universal gates.