The problem has two parts: i. Explain the concept of "Universal Gates" and name two logic gates that are considered universal. ii. Using only NAND gates, design a logic circuit that is equivalent to a NOR gate. Draw the circuit diagram.

1. Problem Description

The problem has two parts:

i. Explain the concept of "Universal Gates" and name two logic gates that are considered universal.

ii. Using only NAND gates, design a logic circuit that is equivalent to a NOR gate. Draw the circuit diagram.

2. Solution Steps

i. Universal Gates:

A universal gate is a logic gate that can implement any Boolean function without needing any other gate type. In other words, any other logic gate (AND, OR, NOT, etc.) can be constructed using only universal gates.

Examples of universal gates are NAND and NOR gates.

ii. Design of a NOR gate using NAND gates:

We need to design a circuit that outputs $overline{A+B}$ using only NAND gates. We can express NOR gate as $overline{A+B} = overline{A} * overline{B}$.

We can create an inverter (NOT gate) using a NAND gate by connecting the two inputs of the NAND gate together. If input is A, output is $overline{A*A} = overline{A}$.

To create NOR using NAND gates:

1. Use NAND gate as NOT gate to invert input A, output is $overline{A}$.

2. Use NAND gate as NOT gate to invert input B, output is $overline{B}$.

3. Use NAND gate with inputs $overline{A}$ and $overline{B}$, output is $overline{overline{A}*overline{B}} = A + B$. Apply another NAND gate acting as NOT gate. The output then becomes $overline{A+B}$.

So, to implement a NOR gate, we need three NAND gates. Two NAND gates will be used as inverters for inputs A and B. The outputs of these two NAND gates will be the inputs to the final NAND gate, which will invert the AND of inverted inputs.

Circuit Diagram:

A --NAND(inputs tied)-->

--NAND--> Output

B --NAND(inputs tied)-->

3. Final Answer

i. A universal gate is a logic gate that can implement any Boolean function without needing any other gate type. NAND and NOR gates are examples of universal gates.

ii. A NOR gate can be implemented using three NAND gates. Two NAND gates are used as inverters for inputs A and B respectively. The outputs of these two NAND gates ($overline{A}$ and $overline{B}$) are then fed as inputs to the third NAND gate. The output of this third NAND gate is $overline{overline{A} * \overline{B}} = A + B$. Another NAND gate as inverter is used to generate $overline{A+B}$.