1.4.3 Boolean Algrebra

“Named after the nineteenth-century mathematician George Boole, Boolean logic is a form of algebra in which all values are reduced to either TRUE or FALSE.”

“Also know as the K-Map, is a method to simplify Boolean algebra expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans’ pattern-recognition capability. They are used to simplify real-word logic requirements so that they can be implemented using a minimum number of physical logic gates.”

“A set of rules for manipulating truth values according to truth tables. Very important in computing as truth values in Boolean algebra are True and false, and can thus easily be represented as the binary digits 1 and 0.”

“Two laws in Boolean algebra which state that AND and OR, or union and intersections, are duel. The rules can be expressed in English as 1) ‘The negation of a conjunction is the disjunction of the negations.’ 2) ‘The negation of a disjunction is the conjunction of the negations.’ Or more informally as 1) “not (A and B)” is the same as “(not A) or (not B)” and also 2) “not (A or B)” is the same as “(not A) and (not B)”. The purpose of De Morgan’s laws is to simplify the design of electronic circuits.”

“A rule or law in Boolean algebra which permits the multiplying or factoring out of an expression.”

“A rule or law in Boolean algebra which permits the removal of brackets from an expression and regrouping of the variables.”

“A rule or law in Boolean algebra which stats that the order of application of two separate terms is not important: A AND B = B AND A.”

“A rule or law in Boolean algebra where if you invert a term twice it is equal to its original term: (NOT NOT A) = A”

“A method of expression Boolean Logic in a diagrammatic form using a set of standard symbols representing the various Logic Gates such as AND NOT OR NAND etc.”

“A notation used in Boolean algebra for defining the output of a logic gate or logic circuit for all possible combinations of inputs.”

“Also known as a data or delay flip flop. This is a circuit or logic design which can be viewed as a memory cell. It has two stable states. Using appropriate input signals, you can trigger the flip-flop from one state to the other.”

“A unit which adds together two input variables. A half adder can only add the inputs together.”

“A unit which adds together two input variables. A full adder can a bit carried from another addition as well as the two inputs.”