Pertemuan:2 (Boolean Algebra and Logic Gates)

11/02/2013 07:22:00 AM (Basic) Digital Technique 0 Comments

In this section, the discusion is about :

• Basic Definitions
• Axiomatic Definition of Boolean Algebra
• Basic Theorems and Properties
• Boolean Functions
• Canonical and Standard Forms
• Other Logic Operations
• Digital Logic Gates
• Integrated Circuits


• Boolean Algebra (formulated by E.V. Huntington, 1904)
A set of elements B={0,1} and two binary operators + and ‧

• Huntington postulates
1. Closure w.r.t. the operator + (‧)
x, y ∈ B ⇒ x+y ∈B; x, y ∈ B ⇒ x‧y ∈B

2. Associative w.r.t. + (‧)
(x+y)+z = x + (y + z); (x‧y)‧z = x ‧ (y‧z)

3. Commutative w.r.t. + (‧)
x+y = y+x; x‧y = y‧x

4. An identity element w.r.t. + (‧)
0+x = x+0 = x; 1‧x = x‧1= x

5. ∀ x ∈ B, ∃ x' ∈ B (complement of x)
x+x'=1; x‧x'=0

6. ‧ is distributive over + : x‧(y+z)=(x‧y)+(x‧z)
+ is distributive over ‧: x+ (y‧z)=(x+ y)‧(x+ z)

Duality principle: remains

Operator Precedence; parenthese, NOT, AND, OR



You can download full chapter from this link: BDT02-Boolean Algebra and Logic Gates