Download BOOLEAN ALGEBRA

BOOLEAN ALGEBRA
One tool to reduce logical expressions is the mathematics of logical expressions, introduced by George
Boole in 1854 and known today as Boolean Algebra.
Boolean Expressions for Logic Gates.
A plus (+) represents an OR operation.
A dot (.) represents an AND operation.
A bar (or a line) above the top of the symbol represents a NOT operation.
A plus (+) sign with a circle around it represents an Exclusive-OR operation.
e.g
Example of equations
S=A
S = A+ B
S = A• B
S = A+ B
S = A• B
S = A⊕ B
S = A• B
S = A• B
S = A • (B + C )
How to read
S is not A
S is A bar
S equals bar A
S equals the inverse of A
S equals the complement of A
S is A or B
S equals A and B
S equals A nor B
S equals the inverse of A or B
S equals A or B all bar
S equals bar open brackets A or B close brackets
S equals A nand B
S equals the inverse of A and B
S equals A and B all bar
S equals bar open brackets A and B close brackets
S equals A xor B
S equals A exclusive or B
S equals not A and B
S equals bar A and B
S equals A and not B
S equals A and open brackets B or C close brackets.
De Morgan’s theorems
Break the bar over the expression and then change the logical operation.
A+ B = A• B
e.g
Exercise:
A• B = A+ B
Write down the following equations written in English phonetic symbols.
esizeIç˘rnÅtbi˘ændsI˘
esi˘kw´lsnÅteIændbi˘ç˘reIændsI˘
esi˘kw´lsbi˘ænd´Up´nbrækItsnÅteIç˘rsI˘kl´UsbrækIts
zedi˘kw´lswaIeksç˘reks
Thierry DROUIN
LTP SAINT GATIEN