الدرس الثالث: النظام الثنائي وتمثيل البيانات في الكمبيوتر

Introduction

This tutorial will guide you through the concepts of the binary system and data representation in computers. Understanding these concepts is fundamental for anyone entering the field of programming or computer science. We will cover how computers work, the differences between decimal and binary systems, and how data is represented, including the ASCII and Unicode standards.

Step 1: Understand How Computers Work

• Computers use a binary system, which consists of two states: 0 and 1.
• These binary digits (bits) represent all types of data in a computer.
• The process of converting human-readable data into binary is crucial for computer operations.

Step 2: Compare Decimal and Binary Systems

• Decimal (base 10) uses digits 0-9, while binary (base 2) uses only 0 and 1.
• Every binary digit represents an increasing power of 2.

Example: The binary number 1011 translates to decimal as follows

• 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0) = 8 + 0 + 2 + 1 = 11

Step 3: Learn About Bits and Bytes

• A bit is the smallest unit of data in a computer, representing a single binary value (0 or 1).
• A byte consists of 8 bits and can represent 256 different values (from 0 to 255).

Step 4: Convert Decimal to Binary

To convert a decimal number to binary

1. Divide the number by 2.
2. Record the remainder (0 or 1).
3. Continue dividing the quotient until it reaches 0.
4. The binary representation is the remainders read in reverse order.

Example: Convert 13 to binary

• 13 / 2 = 6 remainder 1
• 6 / 2 = 3 remainder 0
• 3 / 2 = 1 remainder 1
• 1 / 2 = 0 remainder 1
• Result: 1101

Step 5: Convert Binary to Decimal

To convert binary to decimal

1. Write down the binary number.
2. Assign powers of 2, starting from 0 on the right.
3. Multiply each bit by its corresponding power of 2.
4. Sum all the results.

Example: Convert 1101 to decimal

• 1*(2^3) + 1*(2^2) + 0*(2^1) + 1*(2^0) = 8 + 4 + 0 + 1 = 13

Step 6: Determine the Largest Number in a Byte

• The largest number that can be represented in one byte is 255.
• This is calculated as 2^8 - 1, since a byte consists of 8 bits.

Step 7: Understand ASCII Code

• ASCII (American Standard Code for Information Interchange) represents characters as numbers.
• Each letter, digit, and symbol corresponds to a unique number between 0 and 127.
• Example: The letter 'A' is represented as 65 in ASCII.

Step 8: Learn About Unicode

• Unicode extends beyond ASCII to include characters from many languages and symbols.
• It supports a vast range of characters, making it essential for global applications.

Step 9: Compare ASCII and Unicode

• ASCII is limited to 128 characters, while Unicode can represent over 143,000 characters.
• ASCII is suitable for English text, whereas Unicode accommodates international languages.

Step 10: Homework Assignment

• Practice converting decimal numbers to binary and vice versa.
• Explore the ASCII table linked here: ASCII Table.

Conclusion

In this tutorial, we explored the binary system, how computers represent data, and the importance of ASCII and Unicode. Understanding these concepts is crucial for programming and data manipulation. For further learning, practice conversions and familiarize yourself with the ASCII and Unicode standards.