Boolean Algebra and Number System
A + BC
(A + B)(A + C) =
binary equivalent of 111
01101111
binary equivalent of 184
1011 1000
binary equivalent of 233
11101001
A
A + 0 =
1
A + 1 =
A
A + A
1
A + A'
A + B
A + A'B =
A
A + AB =
0
A . 0 =
A
A . 1 =
A
A . A
0
A . A'
Logic Gate Diagram
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.
Truth Table
A notation used in Boolean algebra for defining the output of a logic gate or logic circuit for all possible combinations of inputs.
Double Negation
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
Distributive
A rule or law in Boolean algebra which permits the multiplying or factoring out of an expression.
Associative
A rule or law in Boolean algebra which permits the removal of brackets from an expression and regrouping of the variables.
Commutative
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.
Boolean Algebra
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.
Boolean Logic
Named after the nineteenth-century mathematician George Boole, it is a form of algebra in which all values are reduced to either TRUE or FALSE.
1. Multiply out (A+B).(B+B ̅) Use identity A ̅+A=1 2. (A+B).1 3. Answer =A+B
Simplify the Equation:
1. Multiply out (B.A)+(B.A.B) 2. Simplify right-hand side (B.A.B) = A.B (B.A)+(A.B) 3. Commutative Law A.B
Simplify the Equation:
1. Use Identity Law A+A = A (A+B).A 2. Multiply out A.A+A.B 3. Use Identity Law A.A = A A+(B.A) 4. Use redundancy law A+(A.B) = A A
Simplify the Equation:
1. Take out the common factor A A(B+1) Use identity 1+A = 1 A(1) or A.1 2. Use identity A.1=A 3. Answer = A
Simplify the Equation: (A.B)+A
De Morgan's Law
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 is to simplify the design of electronic circuits.
