9th Computer Science Unit 2 Binary System Notes

Unit No. 2 Binary System of Class 9th Notes

Introduction of Number Systems

Number systems are fundamental concepts in computer science and mathematics that allow us to represent and manipulate different quantities. Three commonly used number systems are Binary, Decimal, and Hexadecimal.

Binary The binary number system uses only two symbols, 0 and 1, to represent numbers. Each digit in a binary number is a power of 2, starting from the rightmost digit as 2^0. For example, the binary number 1010 is equivalent to (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8 + 0 + 2 + 0 = 10 in the decimal system.

Decimal The decimal number system is the base-10 system we use in our daily lives. It uses ten digits (0 to 9) to represent numbers. Each digit in a decimal number is a power of 10, starting from the rightmost digit as 10^0. For example, the decimal number 342 is equivalent to (3 * 10^2) + (4 * 10^1) + (2 * 10^0) = 300 + 40 + 2 = 342.

Hexadecimal The hexadecimal number system uses sixteen symbols (0 to 9 and A to F) to represent numbers. It is commonly used in computing due to its compact representation of binary data. Each digit in a hexadecimal number is a power of 16, starting from the rightmost digit as 16^0. For example, the hexadecimal number 1A7 is equivalent to (1 * 16^2) + (10 * 16^1) + (7 * 16^0) = 256 + 160 + 7 = 423 in the decimal system.

Long Question Answers of Unit 2 Binary System

MCQ’s and Activities of Unit 2 Binary System

Short Question Answers of Unit 2 Binary System

Number System Conversion

Binary to Decimal To convert a binary number to a decimal number, multiply each digit by its corresponding power of 2 and sum the results. For example, binary number 1101 is equal to (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 8 + 4 + 0 + 1 = 13 in decimal.

Decimal to Binary To convert a decimal number to binary, repeatedly divide the number by 2, and note the remainders in reverse order. For example, decimal number 25 in binary is 11001 (25 ÷ 2 = 12 remainder 1, 12 ÷ 2 = 6 remainder 0, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1).

Decimal to Hexadecimal To convert a decimal number to hexadecimal, repeatedly divide the number by 16, and note the remainders in reverse order. For example, decimal number 255 in hexadecimal is FF (255 ÷ 16 = 15 remainder 15 (F), 15 ÷ 16 = 0 remainder 15 (F)).

Hexadecimal to Decimal To convert a hexadecimal number to decimal, multiply each digit by its corresponding power of 16 and sum the results. For example, hexadecimal number 1A7 is equal to (1 * 16^2) + (10 * 16^1) + (7 * 16^0) = 256 + 160 + 7 = 423 in decimal.

Binary to Hexadecimal To convert a binary number to hexadecimal, group the binary digits into sets of four (starting from the right) and convert each set to its equivalent hexadecimal digit. For example, binary number 11011011 is equal to DB in hexadecimal (1101 – D, 1011 – B).

Hexadecimal to Binary To convert a hexadecimal number to binary, replace each hexadecimal digit with its equivalent four-digit binary representation. For example, hexadecimal number A3 is equal to 10100011 in binary (A – 1010, 3 – 0011).

Memory and Data Storage

Memory In the context of computers, memory refers to the storage location where data and instructions are temporarily stored for processing. It allows the CPU to access data quickly. Computer memory is volatile, meaning it loses its contents when power is turned off.

Representation in Computer Memory Data in computer memory is represented using bits, which are binary digits (0 or 1). A group of 8 bits forms a byte, which is the basic unit of data storage in most computer systems.

Storage Device A storage device is a hardware component that allows for long-term data storage even when the power is off. Examples include hard disk drives (HDDs), solid-state drives (SSDs), and optical discs.

Difference Between Memory and Storage Devices The key difference between memory and storage devices is that memory provides fast access to data for immediate processing by the CPU, while storage devices offer larger capacity for long-term data retention.

Measurement of Size of Computer Memory

Bit The smallest unit of data in a computer, representing either a 0 or a 1.

Byte Consists of 8 bits and is the basic addressable unit of memory.

Kilobyte (KB) Approximately 1,024 bytes.

Megabyte (MB) Approximately 1,024 kilobytes or 1,048,576 bytes.

Gigabyte (GB) Approximately 1,024 megabytes or 1,073,741,824 bytes.

Terabyte (TB) Approximately 1,024 gigabytes or 1,099,511,627,776 bytes.

Petabyte (PB) Approximately 1,024 terabytes or 1,125,899,906,842,624 bytes.

Boolean Algebra

Boolean Proposition A statement that can be either true or false.

Truth Values In Boolean algebra, the truth values are either true (1) or false (0).

Logical Operators Common logical operators include AND (conjunction), OR (disjunction), and NOT (negation).

Truth Tables Truth tables show all possible combinations of truth values for a given logical expression.

Laws of Boolean Algebra Commutative, Distributive, and Associative laws govern the manipulation of logical expressions.

Logical Expressions Logical expressions are combinations of variables and logical operators.

Identity In Boolean algebra, an identity refers to a specific logical equation that holds true under all circumstances, such as the identity laws (A AND 1 = A, A OR 0 = A).

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