Operational Trans conductance Amplifiers:Introduction to Basic Logic Operations.

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Introduction to Basic Logic Operations

In a contemporary digital computer, logic operations for computational tasks are usually done with signals that take values of 0 or 1. These logic operations are performed by many logic networks which constitute the computer. Each logic network has input variables x1, x2, …, xn and output functions f1,f2, . . . , fm. Each of the input variables and output functions take only binary value, 0 or 1. Now let us consider one of these output functions, f. Any logic function f can be expressed by a combination table (also called a truth table) exemplified in Table 26.1.

Basic Logic Expressions

Any logic function can be expressed with three basic logic operations: OR, AND, and NOT. It can also be expressed with other logic operations, as explained in a later section.

Expressions of Logic Functions-0333

Expressions of Logic Functions-0334

Logic Expressions

Expressions with logic operations with AND, OR, and NOT, such as Eq. 26.1, are called switching expressions or logic expressions. Variables x, y, and z are sometimes called switching variables or logic variables, and they assume only binary values 0 and 1. In logic expressions such as Eq. 26.1, each variable, xi, appears with or without the NOT operation, that is, as xi or xi. Henceforth, xi and xi are called the literals of a variable xi.

Logic Expressions with Cubes

Logic expressions such as f = xy ∨ yz ∨ xyz

can be expressed alternatively as a set, {(10-), (-11), (010)},

using components in a vector expression such that the first, second, and third components of the vector represent x, y, and z, respectively, where the value “1” represents xi, “0” represents xi , and “-” represents the lack of the variable. For example, (10-) represents xy . These vectors are called cubes. Logic expressions with cubes are used often because of their convenience for processing by a computer.

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