Demorgan's Theorem Logic Gates

This equation 1 or identity shown above is known as DeMorgans Theorem. De Morgan has suggested two theorems which are extremely useful in Boolean Algebra.

Basic Logic Gates With Truth Tables Digital Logic Circuits Computer Basics Logic Computer Science

DeMorgans Second Theorem states that the NAND gate is equivalent to a bubbled OR gate.

. The two theorems are discussed below. Thus using these conditions we can create truth tables to define operations such as AND AB OR A B and NOT negation. A mathematician named DeMorgan developed a pair of important rules regarding group complementation in Boolean algebra.

The Boolean expression for the NAND gate is given by the equation shown below. Here A and B become input binary variables. These logic gates work on logic operations.

For example A B B AIn Boolean algebra the Logic OR Function follows the Commutative Law the same as for the logic AND function allowing a change in position of. It has been fundamental in the development of digital electronics and is provided for in all modern programming. DeMorgans Law states that the truth of a logical paragraph is preserved when all elements are negated and all unions and intersections are inverted.

0s and 1s are used to represent digital input and output conditions. It is used to analyze and simplify digital circuits or digital gatesIt is also ca lled Binary Algebra or logical Algebra. In a special branch of mathematics known as Boolean algebra this effect of gate function identity changing with the inversion of input signals is described by DeMorgans Theorem a subject to be explored in more detail in a later chapter.

Boolean algebra is the category of algebra in which the variables values are the truth values true and false ordina rily denoted 1 and 0 respectively. By using logic operations as well as truth tables. The Logic OR Function function states that an output action will become TRUE if either one OR more events are TRUE but the order at which they occur is unimportant as it does not affect the final result.

The symbolic representation of the theorem is shown in the figure below. You should recall from the chapter on logic gates that inverting all inputs to a gate reverses that gates essential. By group complementation Im referring to the complement of a group of terms represented by a long bar over more than one variable.

The left hand side LHS of this theorem represents a NAND gate with inputs A and B whereas the right hand side RHS of the theorem represents an OR gate with inverted inputs. The materialist would prove the theorem of Pythagoras by making as many experiments measurements on fuzzy right triangles as many as he needs.

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