Logic Gates and Boolean Algebra Notes

Logic Gates

They are the building blocks of digital circuits.

Basic Gates

There are three basic logic gates:

1. AND Gate

2. OR Gate

3. NOT Gate

Universal Gates

There are two universal gates:

1. NAND Gate

2. NOR Gate

Derived Gates

There are two derived gates:

1. XOR Gate

2. NXOR Gate

De Morgan's Theorems

These theorems describe relationships between AND, OR, and NOT operations:

1. (A+B)' = A' . B'

2. (A.B)' = A' + B'

NAND Gate

• It is an AND gate followed by a NOT gate.

• It can also be called a Bubbled OR Gate.

• A+B = (A.B)'

NOR Gate

• It is an OR gate followed by a NOT gate.

• It can also be called a Bubbled AND Gate.

XOR Gate

• It is also known as EXOR gate.

NXOR Gate

• It is also known as ENXOR gate

Boolean Algebra

Used to analyze and simplify digital logic circuits. Variables can have binary values:

• Binary 1 for high

• Binary 0 for low

Laws

• Commutative Law:

  • A.B = B.A

  • A + B = B + A

• Associative Law:

  • (A.B).C = A.(B.C)

  • (A+B)+C = A+(B+C)

• Distributive Law:

  • A.(B+C) = A.B + A.C

• AND Law:

  • A.0 = 0

  • A.1 = A

  • A.A = A

  • A.A' = 0

• OR Law:

  • A + 0 = A

  • A + 1 = 1

  • A + A = A

  • A + A' = 1

• Inversion Law:

  • (A')' = A

Duality Theorem

Shows the dual relationships in Boolean Algebra.

Karnaugh Maps (K-Map)

Karnaugh Maps are used to simplify Boolean expressions. The transcript mentions K-Maps for 2, 3, and 4 variables, and discusses SOP (Sum of Products) forms.

• In POS, A = 1, A' = 0

• In SOP, A = 0, A' = 1

K-Map with Don't Care Conditions

• Represented by "X" in the cell of the K-Map.

• Can be included or ignored when creating groups for simplification.

Redundant Prime Implicant

P1 = EP1 + RPI