Number System in Computer Science

Computer Number Systems Explained

Fundamentals

Computers fundamentally operate using only 0 and 1. In reality, computers are electronic devices that interpret On (1) and Off (0) states through microscopic switches. These switches toggle to perform operations—enabling tasks when "On" and stopping when "Off."

To process and store data, computers use logic gates (a topic we'll cover later). For now, let's focus on the three primary number systems:

• Binary (Base-2)
• Decimal (Base-10)
• Hexadecimal (Base-16)

Decimal System (Base-10)

The number system humans use daily, based on 10 digits (0–9). When we reach 9, the next number "overflows" to 10 (a combination of 1 and 0 in the next place value).

Example Sequence:

0 1 2 3 4 5 6 7 8 9
10 11 12 ... 19
20 21 ... 29

Key Concept: Each "overflow" adds a new place value (units → tens → hundreds, etc.)

Binary System (Base-2)

Computers use this system with only 0 and 1. After 1, it overflows to 10 (which equals 2 in decimal).

Example Sequence:

0 (0 in decimal)
1 (1)
10 (2)
11 (3)
100 (4)
101 (5)

Critical Note: Binary 10 ≠ Decimal 10. Binary 10 is 2 in decimal.

Hexadecimal System (Base-16)

Used in programming for compact representation. Includes digits 0–9 and letters A–F (where A=10, B=11, ..., F=15). Overflow occurs after F.

Example Sequence:

0 1 2 ... 9 A B C D E F
10 (16 in decimal)
11 (17)
...
1F (31)
20 (32)

Critical Note: Hex 10 ≠ Decimal 10. Hexadecimal 10 is 16 in decimal.

Comparison of Number Systems

Representation	Binary Value	Decimal Value	Hexadecimal Value
10	2	10	16
11	3	11	17
1F	N/A	31	31

Why This Matters

• The same symbol (e.g., "10") represents different values across systems
• Conversion between systems is essential for:
  • Low-level programming
  • Memory addressing
  • Debugging
  • Data representation

(Coming soon: Conversion methods and practical applications!)

Thank you for learning about number systems!