Logic Gates - Digital Logic Design

Logic Gates

Ex NOR function: The NOT exclusive OR function is exclusive NOR function. The output of a 2 input exclusive NOR gate is 1 when both the inputs are 0

or

when both the inputs are 1. If only one of this inputs is at 1, then the output of the exclusive NOR gate is the complement of the exclusive OR gate.

AND gate realization using NAND gate

y = A . B  = output of AND gate

y =   = output of NAND gate

y = A . B = B . A

Realization of OR gate using NAND gate

Y = A + B

Y = A¹ + B¹ = (A¹)¹ + (B¹)¹ = A + B

NOT gate realization using NAND gate

AND gate function realization using NOR gate

y =  = (A¹)¹. (B¹)¹ = A . B

OR gate function realization using NOR gate

y =  = A + B

Realization of Ex –OR gate using NAND gates.

Realization of Ex – OR gate using NOR gate

NON – Degenerate combinations

1. AND – OR circuit is equivalent to NAND – NAND pair
   
   
   
   Let gates 1 and 2 be AND gate and gate 3 be an OR gate. Then
   
   
   y = AB + CD
   
   
   Let gates 1, 2 and 3 be NAND gates. Then
   
   
   Y =  = AB + CD = AB + CD
   
   
   It is seen that the two – level pair AND – OR is equivalent to NAND – NAND pair.
   
   
2. NOR – NOR circuit is equivalent to OR – AND circuit
3. NOT – OR circuit is equivalent to OR – NAND
4. AND – NOR circuit is equivalent to NAND – AND circuits.

Logic gates

In practice, the logic gates used are the AND gate, the OR gate, the NOT gate, the NAND gate, the NOR gate, the exclusive – OR gate.

The AND, OR and NOT gates are called as basic gates.

AND gate:- The symbol used for AND gate is

This gate has a single output and any number of inputs.

OR gate:- The symbol used for OR gate is

NOT gate:

NAND gate: The symbol used for NAND gate is

This gate is equivalent to an AND gate followed by an inverter (NOT gate). A NAND gate must be the exact inverse of an AND gate.

If any of the inputs to a NAND gate is 0, the output of the NAND gate becomes 1. If all the inputs to the NAND gate is are at logical 1, then only the output is 0.

NOR gate: This gate is equivalent to an OR gate followed by an inverter i.e. NOR function is NOT – OR. The NOR gate has in which case the output is 1. In other words, if any of the inputs to a NOR gate is 1, the output is 0.

NAND and NOR gates are called as universal gates because, the basic gate functions are implemented by universal gates.

Ex- OR gate: The name has come about because this gate excludes logic output of 1 for the case when both the inputs are 1.

When odd number of inputs are high. Then the output of the Ex – OR gate goes to high.