What are universal gates? Why are they called so?
Explanation:
In digital electronics, AND, OR, and NOT gates form the basic building blocks of Boolean expressions and logic circuits. However, NAND and NOR gates stand out as they can be arranged in ways that replicate the functions of all basic gates, making them known as universal gates.
NOR Gate as a Universal Gate:
The NOR gate performs the OR operation first and then inverts the result, effectively combining OR and NOT functions. Its output is true only when both inputs are false, which means it’s the opposite of an OR gate. The NOR gate’s Boolean expression is:[latex]Y = (A + B)'[/latex]
where [latex] Y[/latex]is true only when both [latex]A[/latex] and [latex]B[/latex] are false.
Truth Table for NOR Gate:
|
Input A |
Input B |
Output [latex]Y = (A + B)'[/latex] |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
NAND Gate as a Universal Gate:
The NAND gate carries out the AND operation and then inverts the result, combining the functions of AND and NOT. It outputs true in all cases except when both inputs are true. The Boolean expression for the NAND gate is:
[latex]Y = (A \cdot B)'[/latex]
where [latex]Y[/latex] is true unless both [latex]A[/latex] and [latex]B[/latex] are true.
Truth Table for NAND Gate:
|
Input A |
Input B |
Output [latex]Y = (A \cdot B)'[/latex] |
|
0 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
| 1 |
1 |
0 |
Note:
NAND and NOR gates are called universal gates because they can be used to implement the functions of AND, OR, and NOT gates, allowing for the creation of any logic circuit with only one of these gate types.