Скачать или смотреть 9th Computer Science |chapter-2| Lecture 2|Top:Data Representation |PCTB|2025-26

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Key Topics Covered in This Video:
🔹 Introduction to Data Representation
Why do computers use binary to represent data?

The role of transistors in storing data as ON (1) and OFF (0).

How numeric data is stored and processed in a computer's memory.

🔹 Binary Encoding of Integers & Real Numbers
How different sizes of integer values are stored using 1-byte, 2-byte, and 4-byte storage.

Representation of whole numbers in binary.

The concept of signed and unsigned integers in programming.

🔹 Whole Numbers (W) vs. Integers (Z)
✔️ Whole Numbers (W):

A set of non-negative numbers: W = {0, 1, 2, 3, ...}

Used to store values that cannot be negative (e.g., age, number of students).

Understanding 8-bit, 16-bit, and 32-bit whole number storage.

✔️ Integers (Z):

Extends whole numbers to include negative values.

Used in programming to perform calculations that involve negative numbers.

How the sign bit determines positive and negative values.

🔹 Storing Large Numbers in Memory
How computers represent numbers in different storage sizes.

Maximum values for different byte sizes:

1-byte integer (8-bit): 0 to 255 (unsigned) or -128 to 127 (signed).

2-byte integer (16-bit): 0 to 65,535 (unsigned) or -32,768 to 32,767 (signed).

4-byte integer (32-bit): 0 to 4,294,967,295 (unsigned) or -2,147,483,648 to 2,147,483,647 (signed).

🔹 Storing Negative Values: Two’s Complement
How negative numbers are stored in binary format.

Understanding two’s complement representation.

Step-by-step guide to converting a negative decimal number into two’s complement:
1️⃣ Write the positive number in binary.
2️⃣ Invert all the bits (flip 0s to 1s and 1s to 0s).
3️⃣ Add 1 to the least significant bit (LSB).

✔️ Example: Converting -5 to Two’s Complement (8-bit representation)

Write 5 in binary: 00000101

Invert the bits: 11111010

Add 1: 11111011

Final Two’s Complement Representation of -5: 11111011

🔹 Why Two’s Complement is Used?
Eliminates the need for separate addition/subtraction circuits.

Allows simple binary arithmetic with negative numbers.

Used in almost all modern computing architectures.

🔹 Applications of Data Representation in Computing
✔️ How numbers are stored in programming languages (C, Java, Python).
✔️ Understanding integer limits to avoid overflow errors.
✔️ How two’s complement is used in computer memory and CPU operations.