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Class Notes for Basic Logic Gates and Truth Tables, Boolean Algebra | EE 100, Study notes of Electrical and Electronics Engineering

University of Alabama - HuntsvilleElectrical and Electronics Engineering
Prof. Dennis Hite

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

Pre 2010

Uploaded on 07/23/2009

koofers-user-epf
koofers-user-epf ๐Ÿ‡บ๐Ÿ‡ธ

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bg1
Basic Logic Gates and Truth Tables
A F = Aโ€™
0 1
1 0
AAโ€™A F = Aโ€™
0 1
1 0
A F = Aโ€™
0 1
1 0
AAโ€™AAโ€™
A B F = AB
0 0 0
0 1 0
1 0 0
1 1 1
AAB
B
A B F = AB
0 0 0
0 1 0
1 0 0
1 1 1
A B F = AB
0 0 0
0 1 0
1 0 0
1 1 1
AAB
B
AAB
B
A B F = A+B
0 0 0
0 1 1
1 0 1
1 1 1
A
B
A+B
A B F = A+B
0 0 0
0 1 1
1 0 1
1 1 1
A B F = A+B
0 0 0
0 1 1
1 0 1
1 1 1
A
B
A+B
A
B
A+B
XOR gate
B
AF
A B F
0 0 0
0 1 1
1 0 1
1 1 0
XOR gate
B
AF
XOR gate
B
AF
A B F
0 0 0
0 1 1
1 0 1
1 1 0
A B F
0 0 0
0 1 1
1 0 1
1 1 0
A B F = (AB)โ€™
0 0 1
0 1 1
1 0 1
1 1 0
A
B(AB)โ€™
A B F = (AB)โ€™
0 0 1
0 1 1
1 0 1
1 1 0
A B F = (AB)โ€™
0 0 1
0 1 1
1 0 1
1 1 0
A
B(AB)โ€™
A
B(AB)โ€™
A B F = (A+B)โ€™
0 0 1
0 1 0
1 0 0
1 1 0
A
B(A+B)โ€™
A B F = (A+B)โ€™
0 0 1
0 1 0
1 0 0
1 1 0
A B F = (A+B)โ€™
0 0 1
0 1 0
1 0 0
1 1 0
A
B(A+B)โ€™
A
B(A+B)โ€™
pf2

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Download Class Notes for Basic Logic Gates and Truth Tables, Boolean Algebra | EE 100 and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

Basic Logic Gates and Truth Tables

A F = Aโ€™

A A โ€™

A F = Aโ€™

A F = Aโ€™

AA AA โ€™โ€™

A B F = AB

A AB B

A B F = AB

A B F = AB

A AB B

A AB B

A B F = A+B

A

B

A+B

A B F = A+B

A B F = A+B

A

B

A A+B

B

A+B

XOR gate

B

A F

A B F

XOR gate

B

A F

XOR gate

B

A F

A B F

A B F

A B F = (AB) โ€™

A B

(AB) โ€™

A B F = (AB) โ€™

A B F = (AB) โ€™

A B

A (AB) โ€™ B

(AB) โ€™

A B F = (A+B)โ€™

A B

(A+B) โ€™

A B F = (A+B)โ€™

A B F = (A+B)โ€™

A B

(A+B) โ€™

A B

(A+B) โ€™

Boolean algebra

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)

DeMorganโ€™s Theorem

(AB)โ€™ = Aโ€™+Bโ€™ (A+B)โ€™ = Aโ€™Bโ€™

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.

Theorem 6 A*A=A Any variable multiplied by itself will result in the original

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.