What is Binary?

Binary is a base-2 number system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital systems.

In binary:

• Each position represents a power of 2
• The rightmost digit is 2⁰ (1)
• Moving left, each position is the next power of 2: 2¹ (2), 2² (4), 2³ (8), etc.
• A digit of 1 means that power of 2 is included in the sum
• A digit of 0 means that power of 2 is not included

Binary to Decimal Conversion

To convert binary to decimal:

1. Identify the position of each 1 in the binary number (from right to left, starting at 0)
2. Calculate 2 raised to the power of each position
3. Sum all these values

Example: 1010₂

• 1 × 2³ = 1 × 8 = 8
• 0 × 2² = 0 × 4 = 0
• 1 × 2¹ = 1 × 2 = 2
• 0 × 2⁰ = 0 × 1 = 0
• Sum: 8 + 0 + 2 + 0 = 10₁₀

Why Computers Use Binary

• Electronic circuits have two states: on (1) and off (0)
• Binary is reliable and less prone to errors
• It's easier to implement in hardware
• All data in computers is ultimately stored as binary

Common Binary Units

Unit	Size	Description
Bit	1 bit	A single binary digit (0 or 1)
Nibble	4 bits	Half a byte
Byte	8 bits	Can represent 256 values (0-255)
Word	16/32/64 bits	Depends on processor architecture