
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:
10 11 12 ... 19
20 21 ... 29
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:
1 (1)
10 (2)
11 (3)
100 (4)
101 (5)
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:
10 (16 in decimal)
11 (17)
...
1F (31)
20 (32)
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!)
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