CBSE 10th Class Unit 1 - Boolean Logic

 

Boolean Logic

Boolean logic is a system of logic that deals with binary values (True or False, 1 or 0).

Basic Boolean Operations:

• NOT: Inverts the input value.
• NOT 0 = 1
• NOT 1 = 0
• AND: Returns True only if both inputs are True.
• 0 AND 0 = 0
• 0 AND 1 = 0
• 1 AND 0 = 0
• 1 AND 1 = 1
• OR: Returns True if at least one input is True.
• 0 OR 0 = 0
• 0 OR 1 = 1
• 1 OR 0 = 1
• 1 OR 1 = 1
• NAND: Returns the opposite of AND.
• 0 NAND 0 = 1
• 0 NAND 1 = 1
• 1 NAND 0 = 1
• 1 NAND 1 = 0
• NOR: Returns the opposite of OR.
• 0 NOR 0 = 1
• 0 NOR 1 = 0
• 1 NOR 0 = 0
• 1 NOR 1 = 0
• XOR (Exclusive OR): Returns True if only one input is True.
• 0 XOR 0 = 0
• 0 XOR 1 = 1
• 1 XOR 0 = 1
• 1 XOR 1 = 0

Truth Tables

Truth tables show the output of a logic gate for all possible input combinations.

                                                    Truth Tables for AND, OR, NOT, XOR gates

De Morgan's Laws

De Morgan's laws are a set of rules that relate logical operations.

• First Law: NOT (A AND B) = (NOT A) OR (NOT B)
• Second Law: NOT (A OR B) = (NOT A) AND (NOT B)

Logic Circuits

Logic circuits are electronic circuits that implement Boolean functions. They are the building blocks of digital computers.

                                                Logic Gates: AND, OR, NOT, XOR gates