Boolean Algebra Truth Table

Boolean algebra
Boolean algebra is a form of mathematical algebra that is used in digital logic in electronics. It is a two-valued system of algebra that represents logical relationships and operations. The two values used are 1 (true) or 0 (false).

Boolean Expression
A Boolean expression is a statement using Boolean operators that expresses a condition that is either true or false. A Boolean expression always produces a Boolean value. A Boolean expression is composed of a combination of the Boolean constants ( True or False), Boolean variables and logical connectives. Each Boolean expression represents a Boolean function.
Example: AB’C is a Boolean expression.

Boolean Variable
A computer is a binary digital system. Such a system operates on an electronic signal, which has only two possible states: High or 1 and Low or 0. A signal that does not change its state with time is known as constant signal. The value of constant signal always remains the same: either 1 or 0 whereas, a variable signal changes its state with time. The value of the variable signal may be 1 at some point of time and 0 on another. Thus the variables that have only two values 1 and 0 are called Boolean variables or logic variables. These are denoted by A, B, X, Y…..

Logic Function ( Boolean Function)
A logic function is an expression formed by binary variables, binary operators OR, AND, unary operator NOT, parenthesis, and equal sign. For a given value of the variables, the function can be either 0 or 1.
Example: Consider the Boolean Function in an algebraic expression.
F = X.Y.Z’ + X.Y
X,Y,Z are Boolean variables. The right hand side of the above equation is known as expression. Each occurrence of a variable or its complement in an expression is called Literal. In the above expression, there are three variables ( X, Y and Z) and five literals( X, Y, Z’, X, and Y).

Logical Circuit
The high and low level voltage electrical signals are produced by using transistors or ICs or LSIs ( known as logical elements). The circuit composed of logical elements for a specific operation is called logical circuit.

Truth Table
The truth table is a table used to represent Boolean expression of a logic gate function. It shows the output states for every possible combination of input states. The number of rows in a truth table is equal to 2$^n$ ( where n = no.of variables). For example, for 3 inputs variables, no.of rows will be 2$^3$ = 8.

Example: