Digital Logic and Boolean Algebra

In relation to binary, Boolean algebra is a mathematical system for the manipulation of variables that can have one of the two values which are "true" and "false" in formal logic while on and off, or high and low, or 1 and 0 in digital system.

Boolean Functions

-expressions formed with binary variables and Boolean operators that produces an output that is either 1 or 0 and can be represented using Algebraic Expression, Truth Table or Logic Circuit

Example of Boolean Function:

F= A + (A'B)

Evaluating the given example by the given values:

A=0, B=1, x=0, y=0, z=1

F= 0 + (0'•1)

F= 0 + (1•1)

F= 0 + 1

F= 1 

Boolean Operations

Truth Table - shows the relationship between the input values and the result of a Boolean operator or function in tabular form.

Example of a Truth Table:

Digital Logic Circuits

Example:

Simplification of Boolean Functions

-simpler circuit is faster and less expensive 

-reduce the complexity of the ate level implementation and signal propagation delays

-the Laws of Boolean Algebra is applied

Example:

F= A + (A'B)

= (A + A') (A + B) distributive 

= 1 (A + B)             inverse

= A + B                  identity