Number_Systems_Presentation systems conversions
- 1. Number Systems in Computer Science Binary, Decimal, and Hexadecimal Systems with Conversions
- 2. Introduction to Number Systems • Number systems are essential in computer science. • They are used to represent and process data in digital form. • The most commonly used number systems are: • - Binary System • - Decimal System • - Hexadecimal System
- 3. Binary System • • Uses only two digits: 0 and 1 • • Base-2 number system • • Native language of computers • • 1 represents ON state; 0 represents OFF state • • Example: 1010 (binary)
- 4. Decimal System • • Uses ten digits: 0 to 9 • • Base-10 number system • • Most common number system used by humans • • Example: 245 (decimal)
- 5. Hexadecimal System • • Uses sixteen digits: 0–9 and A–F • • Base-16 number system • • Often used in programming and computer memory addressing • • Example: 1A3F (hexadecimal)
- 6. Binary to Decimal Conversion • To convert binary to decimal: • • Multiply each bit by 2 raised to the power of its position (right to left, starting from 0) • • Sum all the results • Example: • Binary: 1011 • = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ • = 8 + 0 + 2 + 1 = 11 (decimal)
- 7. Decimal to Binary Conversion • To convert decimal to binary: • • Divide the number by 2 repeatedly • • Write down the remainders • • Read the remainders in reverse order • Example: • Decimal: 13 • 13 ÷ 2 = 6 remainder 1 • 6 ÷ 2 = 3 remainder 0 • 3 ÷ 2 = 1 remainder 1