Universal Gates

  1. Example
  2. Using NAND gates
  3. Using NOR gates
  4. Implementation of a logic function using NAND

Universal gates are digital logic gates that can be used to implement any Boolean function without requiring other gates. In other words, any Boolean function can be expressed as a combination of one or more universal gates. The two most commonly used universal gates are the NAND gate and the NOR gate.

Example

The NAND gate (Not-AND) is a digital logic gate that outputs a low state (0) only when all its inputs are high states (1), otherwise, it outputs a high state (1). The NAND gate can be used to implement all the basic gates like AND, OR, and NOT.

The NOR gate (Not-OR) is a digital logic gate that outputs a high state (1) only when all its inputs are low states (0), otherwise, it outputs a low state (0). The NOR gate can be used to implement all the basic gates like AND, OR, and NOT. Using universal gates, we can implement any digital circuit regardless of its complexity. A circuit that uses only NAND gates is called a NAND logic circuit, and a circuit that uses only NOR gates is called a NOR logic circuit. Since NAND and NOR gates are the simplest form of universal gates, they are often used in the design and implementation of digital circuits.

In practical implementation, other digital logic gates such as XOR, XNOR, and buffer gates are also used along with universal gates to improve the performance and efficiency of digital circuits.

Using NAND gates

The NAND gate is a universal gate, which means that any logic function can be implemented using only NAND gates. Here's how to get NOT, AND and OR using NAND gates:

  • NOT gate using NAND gates: A NOT gate can be implemented using a single NAND gate. The output of the NAND gate is the complement of its inputs. Thus, connecting both inputs of a NAND gate together, the output will be the complement of the input. This forms the NOT gate.
  • AND gate using NAND gates : An AND gate can be implemented using two cascaded NAND gates. The output of the first NAND gate is the complement of the first input and the second input is fed directly to the second NAND gate. The output of the second NAND gate is the complement of the AND of the two inputs, which is the desired output of the AND gate.
  • OR gate using NAND gates : An OR gate can be implemented using three cascaded NAND gates. The inputs are first inverted using two NAND gates connected as a NOT gate. The inverted inputs are then fed into another NAND gate, which implements the AND operation on the inverted inputs. The output of this AND gate is then inverted again using another NAND gate, resulting in the desired output of the OR gate.

Using NOR gates

We can use NOR gates to implement basic logic functions as follows:

  • NOT gate using NOR gate : The NOT gate can be implemented using a single NOR gate as follows:
    • 	Input: A
	Output: NOT(A)

	NOR gate implementation: Output = A NOR A = NOT(A)
  • AND gate using NOR gate: : The AND gate can be implemented using two NOR gates as follows:
    •   	Inputs: A, B
	Output: A AND B

	NOR gate implementation: Output = NOT(A NOR B) = A AND B
  • OR gate using NOR gate : The OR gate can be implemented using three NOR gates as follows:
    • 	Inputs: A, B
	Output: A OR B

	NOR gate implementation: Output = NOT(NOT(A) NOR NOT(B)) = A OR B

Note that these implementations using NOR gates are equivalent to the implementations using NAND gates.

Implementation of a logic function using NAND

Here is an example of a logic implementation using only NAND gates. Let's say we want to implement the following logic function:

F(A, B, C) = (A AND B) OR (NOT C)

We can implement this function using only NAND gates in the following way:

  1. Implement AND gate using NAND gates:
    2.   A AND B = NOT (A NAND B)
  2. Implement NOT gate using NAND gates:
    3.   NOT X = X NAND X
  3. Implement OR gate using NAND gates:
    4.   X OR Y = (NOT X) NAND (NOT Y)

Using the above gate implementations, we can implement the original logic function as follows:

F(A, B, C) = ((A NAND B) NAND (A NAND B)) NAND (C NAND C)

Alternatively, we can simplify the above expression using De Morgan's law and arrive at:

F(A, B, C) = (A NAND A) NAND (B NAND B) NAND (C NAND (A NAND B))

Both implementations will produce the same output as the original function.