Binary Bits of Zeros and Ones Because there are only two valid Boolean values for representing either a logic “1” or a logic “0”, makes the system of using Binary Numbers ideal for use in digital or electronic circuits and systems. A binary number system uses both of these two states.

Definition: In digital electronics, the number system is used for representing the information. The number system has different bases and the most common of them are the decimal, binary, octal, and hexadecimal. The base or radix of the number system is the total number of the digit used in the number system.

Computer circuits are built from simple elements called “gates,” made from either mechanical or electronic switches. They operate according to Boolean algebra to determine the value of an output signal (one or zero), or to save a value in a “flip-flop,” a storage unit built from several gates.

In Minterm, we look for the functions where the output results in “1” while in Maxterm we look for function where the output results in “0”. We perform Sum of minterm also known as Sum of products (SOP) . We perform Product of Maxterm also known as Product of sum (POS).

A prime implicant of a function is an implicant (in the above particular sense) that cannot be covered by a more general, (more reduced – meaning with fewer literals) implicant.

A product term is an implicant of a function if the function has the value ‘1’ for all minterms of the product term. • Prime implicant If the removal of any literal from an implicant P results in a product term that is not an implicant of the function then P is a prime implicant.

A group of square or rectangle made up of bunch of adjacent minterms which is allowed by definition of K-Map are called prime implicants(PI) i.e. all possible groups formed in K-Map. These are those subcubes(groups) which cover atleast one minterm that can’t be covered by any other prime implicant.

A Karnaugh map (K-map) is a pictorial method used to minimize Boolean expressions without having to use Boolean algebra theorems and equation manipulations. A K-map can be thought of as a special version of a truth table . Using a K-map, expressions with two to four variables are easily minimized.

The “Don’t care” condition says that we can use the blank cells of a K-map to make a group of the variables. To make a group of cells, we can use the “don’t care” cells as either 0 or 1, and if required, we can also ignore that cell.

A Don’t Care cell can be represented by a cross(X) in K-Maps representing a invalid combination. For example, in Excess-3 code system, the states 0000, 0001, 0010, 1101, 1110 and 1111 are invalid or unspecified. These states are called don’t cares.

Pairs, Quads, and Octets Quad: A group of 4 one’s that are horizontally or vertically adjacent. End to end or in form of a square. A quad eliminates two variables and their complements. An octet eliminates three variables and their complements.

An Incompletely specified function is a Boolean function that only define output values for a subset of its inputs – i.e. a Boolean function whos output is a don’t care for at least one of its input combinations. Incompletely specified functions often make no guarantees as to the unspecified output whatsoever.

Incompletely specified functions, also known as can’t happen conditions, is a situation that sometimes occurs when certain combinations of the variables of a function cannot occur. For these combinations we can select the value of the function to be 0 or 1; whichever leads to the more minimal solution.

In digital logic, a don’t-care term (abbreviated DC, historically also known as redundancies, irrelevancies, optional entries, invalid combinations, vacuous combinations, forbidden combinations, unused states or logical remainders) for a function is an input-sequence (a series of bits) for which the function output …

Don’t care values result when certain assignments of values. to variables never occur. For example, The designer can expect that the assignments ABCD =