Canonical Representation

As it turns out, every boolean function can be expressed using at least one boolean expression called
the canonical representation, Starting with the function's truth table, we focus on all the rows in
which the function has value 1. For each such row, we construct a term created by And-ing together literals
(variables or their negations) that fix the values of all the row's inputs.

Gate logic

gate is a physical device that implements a Boolean function. If a Boolean function f operates on n variables and returns m binary results, the gate that implements f will have n input pins and m output pins. Just like complex boolean functions can be expressed in terms of simpler functions, complex gates are composed from more elementary gates. The simplest gates of all are made from tiny switching devices, called transistors, wired in a certain topology designed to effect the overall gate functionality.

Boolean Expressions

In addition to the truth table specification, a boolean function can also be specified using boolean operations over its input variables. The basic boolean operators used today are: AND, OR, and NOT.

Truth Table Representation

The easiest way to specify a boolean function is to enumerate all the possible values of the function's input variables, aswell as the function's output for each set of inputs. This is referred as a truth table representation of a function.

Boolean Algebra

   Boolean algebra deals with boolean or binary values that are usually true or false, 1 or 0, yes or no etc.. We will stick with using 1 and 0. A boolean function operates on binary inputs and returns binary outputs. Since computer hardware is based on binary value manipulation, boolean functions play a key role in the specification, construction, and optimization of hardware architectures.

Boolean Logic pt 2

   We start out with one primitive logic gate _ NAND _ and build all other logic gates from it. The result is a rather standard set of gates, that will be used to construct our computer's processing and storage chips.

Boolean Logic pt 1

   Every personal device, be it a personal computer, a cellular telephone, or a network router, is based on a set of chips designed to store and process information. Although these chips come IM different shapes and forms, they are all made from the same building blocks: Elementary logic gates. The gates can be physically implemented in many different materials and fabrication techniques, but their logical behavior is consistent across all computers.