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In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.Instead of elementary algebra where the values of the variables are numbers, and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction and denoted ...

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.

J.J. Shann 2 2 Chapter Overview 2 1 Binary Logic and Gates 2 2 Boolean Algebra 2 3 Standard Forms 2 4 Two Level Circuit Optimization 2 5 Map Manipulation

Boolean algebra is a different kind of algebra or rather can be said a new kind of algebra which was invented by world famous mathematician George Boole in the year of 1854. He published it in his book “An Investigation of the Laws of Thought”. Later using this technique Claude Shannon introduced a new type of algebra which is termed as Switching Algebra.

Circuit Schematic: This circuit is a simple 3 variable Boolean expression minimizer. It uses the Quine McCluskey algorithm which was described in the chapter 1.In this the microcontroller plays a major role, it consists of code to implement the described algorithm as well as controlls other components in the circuit.

In designing digital circuits, the designer often begins with a truth table describing what the circuit should do. The design task is largely to determine what type of circuit will perform the function described in the truth table.

Giving the Boolean expression of: Q = AB AB The logic function implemented by a 2 input Ex NOR gate is given as “ when both A AND B are the SAME ” will give an output at Q.In general, an Exclusive NOR gate will give an output value of logic “1” ONLY when there are an EVEN number of 1’s on the inputs to the gate (the inverse of the Ex OR gate) except when all its inputs are “LOW”.

1 Chapter 2 Boolean Algebra and Logic Gates The most common postulates used to formulate various algebraic structures are: 1. Closure. N={1,2,3,4…}, for any a,b N we obtain a unique c N by the operation a b=c.

Note that the result from casting any non BLOB value into a BLOB and the result from casting any BLOB value into a non BLOB value may be different depending on whether the database encoding is UTF 8, UTF 16be, or UTF 16le. Boolean Expressions

binational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are “combined” or connected together to produce more complicated switching circuits. These logic gates are the building blocks of combinational logic circuits. An example of a combinational circuit is a decoder, which converts the binary code data present at its input into a number of different output ...