Computer Technology - Number Systems (Base 2, Base 10, Base 8, Base 16)

Computers use different number systems to represent and process data. Each number system is based on a specific base, which determines the digits used and how values increase. Although all number systems follow the same concept, they differ in their base and how numbers are represented.

1. Base 2 (Binary)

Binary is the number system used by computers internally.

• Digits used: 0, 1
• Base: 2
• Place values: Powers of 2 (1, 2, 4, 8, 16, ...)

Each position in a binary number is 2 times larger than the previous one.

Example:

Binary 1011
= (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
= 11 (decimal)

Use: All computer data, including text, images, and programs, is stored in binary form.

2. Base 10 (Decimal)

Decimal is the number system used in everyday life.

• Digits used: 0–9
• Base: 10
• Place values: Powers of 10 (1, 10, 100, 1000, ...)

Each position is 10 times larger than the previous one.

Example:

345
= (3 × 100) + (4 × 10) + (5 × 1)

Use: Human counting, calculations, and everyday use.

3. Base 8 (Octal)

Octal is a simplified way of representing binary numbers.

• Digits used: 0–7
• Base: 8
• Place values: Powers of 8 (1, 8, 64, 512, ...)

Each position is 8 times larger than the previous one.

Example:

17 (octal)
= (1 × 8) + (7 × 1)
= 15 (decimal)

Use: Sometimes used in computing systems, such as file permissions.

4. Base 16 (Hexadecimal)

Hexadecimal is a compact and human-friendly way to represent binary data.

• Digits used: 0–9 and A–F
• Letter values: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15
• Base: 16
• Place values: Powers of 16 (1, 16, 256, 4096, ...)

Each position is 16 times larger than the previous one.

Example:

1A (hex)
= (1 × 16) + (10 × 1)
= 26 (decimal)

Use: Widely used in programming, memory addresses, and color codes.