Introduction to Logic Gate:

We have set of basic principles of logic. Any Boolean algebra operation can be associated with inputs and outputs represent the statements of Boolean algebra. Although these circuits may be complex, they may all be constructed from three basic devices. We have three different types of logic gates .These are the AND gate, the OR gate and the NOT gate.

 

Simple logic gates:

 

  • NOT gate gives a 1 when input A is 0.
  • AND gate gives a 1 when both A AND B are 1.
  • OR gate gives a 1 when A OR B are 1 or both.
  • NOR gate gives a 1 when both A and B are 0.
  • The NAND gate gives a 1 when either A or B are 0.


How to combining logic gates:

Truth table is commonly used to make for simple combinations.

And then the output of one logic gate can be related to the input of another logic gates.

This is the example: The output of one logic gate can be related to the input of another. And here we are using a NAND gate with a NOT gate.

 

Introduction of boolean algebra:

 

An algebraic system of logic introduced by George Boolein 1854.The fundamental rules for simplifying and combining logic gates are called Boolean algebra. The rules are commonly used to simplify the long expressions. Boolean 0 and 1 do not stand for actual numbers but instead represent the status, or logical level.

Example 1:

Consider the AND gate where one of the inputs is 1. By using thetruth table, study the possible outputs and hence simplify the Expression x · 1.

Solution: Starting the truth table for AND, we see that if x is 1 then1 · 1 = 1, while if x is 0 then 0 · 1 = 0. This can be summarized in the rule that x · 1 = x.

Boolean algebra rules:

The rules are commonly used to complete different operations. The rules are derived from logic gates.