Explain De Morgan's theorem
Answers
Answer:
DeMorgan's Theory
DeMorgan's TheoryDeMorgan's first theorem states that two (or more) variables NOR´ed together is the same as the two variables inverted (Complement) and AND´ed, while the second theorem states that two (or more) variables NAND´ed together is the same as the two terms inverted (Complement) and OR´ed.
Answer:
As we have seen previously, Boolean Algebra uses a set of laws and rules to define the operation of a digital logic circuit with “0’s” and “1’s” being used to represent a digital input or output condition. Boolean Algebra uses these zeros and ones to create truth tables and mathematical expressions to define the digital operation of a logic AND, OR and NOT (or inversion) operations as well as ways of expressing other logical operations such as the XOR (Exclusive-OR) function.
While George Boole’s set of laws and rules allows us to analyise and simplify a digital circuit, there are two laws within his set that are attributed to Augustus DeMorgan (a nineteenth century English mathematician) which views the logical NAND and NOR operations as separate NOT AND and NOT OR functions respectively.
But before we look at DeMorgan’s Theory in more detail, let’s remind ourselves of the basic logical operations where A and B are logic (or Boolean) input binary variables, and whose values can only be either “0” or “1” producing four possible input combinations, 00, 01, 10, and 11.
Truth Table for Each Logical Operation
Input Variable Output Conditions
A B AND NAND OR NOR
0 0 0 1 0 1
0 1 0 1 1 0
1 0 0 1 1 0
1 1 1 0 1 0
The following table gives a list of the common logic functions and their equivalent Boolean notation where a “.” (a dot) means an AND operation, a “+” (plus sign) means an OR operation, and the complement or inverse of a variable is indicated by a bar over the variable.