DIGITAL LOGIC GATES

DIGITAL LOGIC GATES
As Boolean functions are expressed in terms of AND, OR, and NOT operations, it is easier to implement the Boolean functions with these basic types of gates. However, for all practical purposes, it is possible to construct other types of logic gates. The following factors are to be considered for construction of other types of gates.
1. The feasibility and economy of producing the gate with physical parameters.
2. The possibility of extending to more than two inputs.
3. The basic properties of the binary operator such as commutability and associability.
4. The ability of the gate to implement the Boolean functions alone or in conjunction
with other gates.
There are eight functions—Transfer (or buffer), Complement, AND, OR, NAND, NOR, Exclusive-OR (XOR), and Equivalence (XNOR) that may be considered to be standard gates in digital design.
The transfer or buffer and complement or inverter or NOT gates are unary gates, i.e., they have single input, while other logic gates have two or more inputs.
Extension to Multiple Inputs
A gate can be extended to have multiple inputs if its binary operation is commutative and associative. AND and OR gates are both commutative and associative.
For the AND function, AB = BA -commutative
and
(AB)C = A(BC) = ABC. -associative
For the OR function, A + B = B + A -commutative
and
(A + B) + C = A + (B + C). -associative
These indicate that the gate inputs can be interchanged and these functions can be extended to three or more variables very simply as shown in Figures 2.13(a) and 2.13(b).