NAND Circuits

NAND Circuits

 The NAND gate is said to be a  universal gate because any logic circuit can be implemented with it. To show that any Boolean function can be implemented with NAND gates, we need only show that the logical operations of AND, OR, and complement can be obtained with NAND  gates alone. This is indeed shown in  Fig. 3.16.The complement operation is obtained from a one-input NAND gate that behaves exactly like an inverter. The AND operation requires two NAND gates. The first produces the NAND operation and the second inverts the logical sense of the signal. The OR operation is achieved through a NAND gate with additional inverters in each input.

A convenient way to implement a Boolean function with NAND gates is to obtain the simplified Boolean function in terms of Boolean operators and then convert the function to NAND logic.The conversion of an algebraic expression from AND, OR, and complement to NAND can be done by simple circuit manipulation techniques that change AND–OR diagrams to NAND diagrams.

 To facilitate the conversion to NAND logic, it is convenient to define an alternative graphic symbol for the gate. Two equivalent graphic symbols for the NAND gate .