4.1.9. Complete Set of Operators

Now we are talking about this particular logic gate here we are having two terms called complete set of operators and I think you may be knowing about these things so the complete set of operators are nothing but AND, OR and NOT gate.

In digital logic, a complete set of operators refers to the fundamental logic gates required to perform any logical operation. These gates are AND, OR, and NOT. Understanding these gates is crucial because with just these three gates, all other logic gates can be constructed. For instance, NOR and XOR can be derived from combinations of AND, OR, and NOT gates.

Think of the complete set of operators like the basic ingredients required for cooking. Just as you can prepare numerous dishes using a few fundamental ingredients like salt, pepper, and oil, in digital logic, you can create complex circuits using just AND, OR, and NOT gates.

Along with that we are having another terms called universal gates. So, NAND and NOR are treated as universal gates, Why you say these are the universal gates? Any digital logic circuit can be implemented with the help of only NAND gate or only NOR gate.

NAND and NOR gates are referred to as universal gates because you can use them to create any other type of logic gate, including AND, OR, and NOT gates. This means that any digital circuit can be constructed using exclusively NAND or exclusively NOR gates. This property makes them extremely valuable in digital design and compact circuit implementations.

Consider NAND and NOR gates as Swiss Army knives in digital electronics. Just as a Swiss Army knife contains various tools like a knife, screwdriver, and scissors all in one tool, both NAND and NOR gates can perform multiple functions in a circuit by combining them in different ways.

if I don’t have this particular gate then what will happen with the help of NOT, AND, and OR gate I can have the effect of this particular gates.

When designing digital circuits, if we cannot directly utilize a specific gate type, we can still achieve the same functionality by combining AND, OR, and NOT gates. For example, an XOR gate can be created using AND, OR, and NOT gates by following the logical expressions that define an XOR function. This flexibility is crucial in circuit design.

Imagine you want to bake a cake, but you lack a mixer. Instead of abandoning the recipe, you can use a whisk to mix ingredients by hand. In digital logic, even if a specific gate isn't immediately available, you can 'mix' logic functions using the fundamental gates to create the desired outcome.

Now, as an assignment you just think how to be implement this particular function with the help of only AND gate, NOR gate or NAND gate just take as a assignment and just see how the circuit can be implemented with the help of only NAND gate or with the help of NOR gate.

As a practical exercise, students are encouraged to take any logic function and implement it using only universal gates like NAND or NOR. This assignment helps solidify understanding of how these gates can replicate other logical functions and reinforces the idea of universality in digital logic.

Think of this assignment like solving a puzzle. You have a picture (the function) that needs to be completed using only specific puzzle pieces (the universal gates). This practice sharpens problem-solving skills and enhances creativity in circuit design.

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