On completion of this module, you will be able to:

• Understand logic gates
• Understand symbolic and truth table representation of logic gates
• Understand simplification of Boolean expressions using logic gates
• Understand universal gates

Logic Gates

• Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output.
• Logic gates is a digital circuit that follows certain logical relationship between the input and output. Therefore, they are generally known as logic gates, because they control the flow of information.
• The above said logic gates can be classified into following categories:
  1. Basic Gates :- (a) AND Gate (b.) OR Gate (c.) NOT Gate
  2. Universal Gates :- (a.) NAND Gate (b.) NOR Gate
  3. Combinational Gates:- (a.) X – OR Gate (b.) X – NOR Gate
  
• The basic operations are described below with the aid of truth tables.

Rules of Boolean Algebra

• Boolean Algebra rules are useful in manipulating and simplifying Boolean expressions.
• Rules 1 through 9 will be viewed in terms of their application to logic gates. Rules 10 through 12 will be derived in terms of the simpler rules.

• In the above table A, B, or C can represent a single variable or a combination of variables.

Example 1: Using Boolean algebra techniques, simplify this expression: AB + A(B + C) + B(B + C)

Solution:

• Step 1: Apply the distributive law to the second and third terms in the expression, as follows:
  AB + AB + AC + BB + BC
• Step 2: Apply rule (BB = B) to the fourth term.
  AB + AB + AC + B + BC
• Step 3: Apply rule (AB + AB = AB) to the first two terms.
  AB + AC + B + BC
• Step 4: Apply rule (B + BC = B) to the last two terms.
  AB + AC + B
• Step 5: Apply rule (AB + B = B) to the first and third terms.
  B+AC
• At this point the expression is simplified as much as possible.

Example 2:

Solution:

Example 3: Simplify the below equation

Solution:

Example 4: Show that A + A.B = A

Solution: