In addition to AND, OR, and NOT gates, other logic gates like NAND and NOR are also used in the design of digital circuits.
There are two types of Universal gates:
1. NAND gate.
2. NOR gate.
* In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate and are the basic gates used in all IC digital logic families.
* In fact, an AND gate is typically implemented as a NAND gate followed by an inverter not the other way around!!
* Likewise, an OR gate is typically implemented as a NOR gate followed by an inverter not the other way around!!
* 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.
* The output is high any time atleast one of the input is low.
* Truth table of NAND gate is as follows:
NAND Gate is a Universal Gate:
To prove that any Boolean function can be implemented using only NAND gates, we will show that the AND, OR, and NOT operations can be performed using only these gates.
Implementing an Inverter Using only NAND Gate
The figure shows two ways in which a NAND gate can be used as an inverter (NOT gate).
1. All NAND input pins connect to the input signal A gives an output A’.
2. One NAND input pin is connected to the input signal A while all other input pins are connected to logic 1. The output will be A’.
Implementing AND Using only NAND Gates
An AND gate can be replaced by NAND gates as shown in the figure (The AND is replaced by a NAND gate with its output complemented by a NAND gate inverter).
Implementing OR Using only NAND Gates
An OR gate can be replaced by NAND...