# Digital Logic Gates || Boolean Algebra and Logic Gates || Bcis Notes

## Digital Logic Gates

Digital Logic Gates are the representation of signals and sequences of a digital circuit through numbers. It is the basis for digital computing and provides a fundamental understanding of how circuits and hardware communicate within a computer. Digital logic is typically embedded into most electronic devices, including calculators, computers, video games, and watches. This field is utilized by many careers that work with computers and technology, such as engineers and repair technicians. Factors to be weighed when considering the construction of other types of logic gates are:
  The feasibility and economy of producing the gate with physical components
 The possibility of extending the gate to more than two inputs
 The basic properties of the binary operator such as commutativity and associativity, and
 The ability of the gate to implement Boolean functions alone or in conjunction with other gates.
Of the 16 functions defined in Table above, two are equal to a constant and four others are repeated twice. There are only ten functions left to be considered as candidates for logic gates. Two, inhibition and implication, are not commutative or associative and thus are impractical to use as standard logic gates. The other eight: complement, transfer, AND, OR, NAND, NOR, exclusive-OR, and equivalence, are used as standard gates in digital design.

Fig: Binary logic gates

## Universal Logic Gates

A universal logic gate is a logic gate that can be used to construct all other logic gates. There are many articles about how NAND and NOR are universal gates, but many of these articles omit other gates that are also universal gates. This article covers two-input logic gates, demonstrates that the NAND gate is a universal gate, and demonstrates how other gates are universal gates that can be used to construct any logic gate.

NAND Gate is a Universal Gate
NAND gates can be connected to form any other logic gates. Figures 1,2,3 show how NAND gates can be connected to form INVERTER, AND, and OR gates. These gates can be combined to form the other logic gates.

## NOR gate as a universal gate:

We have seen how the NAND gate can be used to make all the three basic gates by using that alone. Now we will discuss the same in case of NOR gate.

The above diagram is of an OR gate made by only using NOR gates. The output of this gate is exactly similar to that of a single OR gate. We can see the circuit arrangement of OR gate using, NOR gate is similar to that of AND gate using NAND gates.

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