

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Material Type: Notes; Professor: Hite; Class: FUND COMP, ELEC & OPT ENGR; Subject: Electrical Engineering; University: University of Alabama - Huntsville; Term: Unknown 1989;
Typology: Study notes
1 / 2
This page cannot be seen from the preview
Don't miss anything!
A AB B
A AB B
A AB B
A
B
A+B
A
B
A A+B
B
A+B
XOR gate
B
A F
XOR gate
B
A F
XOR gate
B
A F
A B
(AB) โ
A B
A (AB) โ B
(AB) โ
A B
(A+B) โ
A B
(A+B) โ
A B
(A+B) โ
Basic Operations of Boolean algebra Compliment Notation
0 โ = 1 (read as NOT 0 is equal to 1) 1 โ = 0 (read as NOT 1 is equal to 0)
If A=1 then A โ = If A โ =1 then A= Therefore (A โ ) โ = A
Multiplicative Behavior: (AND Gates)
00 = 0 01 = 0 1*1 = 1
Additive Behavior (OR Gates)
0 + 0 = 0 0 + 1 = 1 1 + 1 = 1
Important Laws of Boolean algebra
Commutative Laws
AB = BA A+B = B+A
Associative Laws
(AB)C = A(BC) (A+B)+C = A+(B+C)
Distributive Laws
A(B+C) = AB + AC A+BC = (A+B)(A+C)
DeMorganโs Theorem
(AB)โ = Aโ+Bโ (A+B)โ = AโBโ
Some Basic Boolean algebra Theorems
Theorem 1 A+0=A If zero is added to a variable, the result will be the value stored in the variable. Theorem 2 A+1=1 If one is added to a variable, the result will always be one.
Theorem 3 A+A=A Any variable added to itself will result in the original variable. If A=1, the result would be 1+1 = 1, if A=0, the result would be 0+0 = 0. Theorem 4 A*1=A A variable multiplied by one will be unchanged.
Theorem 5 A*0=0 A variable multiplied by zero results in zero.
variable. If A=1, the result would be 11 = 1, if A=0, the result would be 00 = 0. Theorem 7 (A โ ) โ =A Complimenting a variable twice yields the original variable.
Theorem 8 A+A โ =1 A variable added to its compliment is always 1. If A=0, 0+1=1, if A=1, 1+0=1. Theorem 9 AA โ =0 A Variable multiplied by its compliment is always 0. If A=0, 01=0, if A=1, 1*0=0.