Realization of logic gate using universal gates - mbits-mirafra/digitalDesignCourse GitHub Wiki

Why called universal?

Because any basic gates can be implemented using these logic gates.

Why universal gates are preferred in logic design?

When compared with basic gates these gates operate faster because of lesser resistance hence lesser delay.

NAND and NOR gates are called universal gates because they can be combined to produce any of the other gates like OR, AND, and NOT gates.

Implementation of NOT gate

1. using NAND gates

2. using NOR gates

Implementation of AND gate

1. using NAND gates

2. using NOR gates

Implementation of OR gate

1. using NAND gates

2. using NOR gates

Implementation of XOR gate

To implement XOR first take double complement and solve using De-Morgans theorem

   To represent using NAND gates, write in SOP form
   Y=((A'B+AB')')'
   Y=((A'B)'.(AB')')'

   To represent using NOR gates, write in POS form
   Y=((A'B+AB')')'
   Y=((A'B)'.(AB')')'
   Y=((A+B').(A'+B))'

The above two representations of XOR gates can be optimized using boolean algebra as shown in below logic circuit.

1. using NAND gates

2. using NOR gates

Implementation of XNOR gate

Similarly take double complement of the XNOR equation and apply De-Morgan's theorem.(Refer above example of XOR gates)

   To represent using NAND gates, write in SOP form
   To represent using NOR gates, write in POS form

After implementing using the above mentioned method we get a circuit, which can be further optimized as shown below.

1. using NAND gates

2. using NOR gates

Implementation of NOR using NAND gate

Implementation of NAND using NOR gate