Binary Number System Guide
A comprehensive guide to understanding the binary (base-2) number system.
What is Binary?
The binary number system (base-2) uses only two digits: 0 and 1. It is the fundamental language of computers and digital electronics. Every piece of data — text, images, video, software — is ultimately stored and processed as sequences of binary digits (bits).
Place Values
In binary, each position represents a power of 2 (just as each position in decimal represents a power of 10):
| Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Power of 2 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Converting Binary to Decimal
Multiply each bit by its position value and sum the results:
1101₂ = (1×8) + (1×4) + (0×2) + (1×1)
= 8 + 4 + 0 + 1
= 13₁₀
Common Binary Values
1
1
2
10
4
100
8
1000
16
10000
32
100000
64
1000000
128
10000000
255
11111111
256
100000000
512
1000000000
1024
10000000000