Binary, Hex, and Decimal Explained

Number systems overview

A number system is defined by its base — how many unique digits it uses before rolling over. Decimal (base-10) uses 0–9. Binary (base-2) uses 0–1. Hexadecimal (base-16) uses 0–9 and A–F.

How binary works

Each binary digit (bit) represents a power of 2, from right to left:

Binary: 1 0 1 1 0 1
         ↓ ↓ ↓ ↓ ↓ ↓
Power: 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
        32  16  8   4   2   1

= 32 + 0 + 8 + 4 + 0 + 1 = 45

So 101101 in binary = 45 in decimal

How hexadecimal works

Hex uses base-16. Each hex digit represents a power of 16. Letters A–F represent 10–15:

Hex: 2 F A
      ↓  ↓  ↓
    16² 16¹ 16⁰
    256  16   1

= (2 × 256) + (15 × 16) + (10 × 1)
= 512 + 240 + 10
= 762

So 0x2FA in hex = 762 in decimal

One hex digit = exactly 4 binary digits. This is why hex is so useful: FF in hex = 11111111 in binary = 255 in decimal. Two hex digits always represent one byte.

Where each is used

Frequently asked questions

Why do computers use binary?

Because electronic circuits have two stable states: on (1) and off (0). It's physically easier and more reliable to distinguish between two states than ten. All the complexity of modern computing — images, video, AI — is ultimately billions of on/off switches operating very fast.

What is a bit, byte, and word?

A bit is one binary digit (0 or 1). A byte is 8 bits (can represent 0–255). A word is architecture-dependent: typically 32 bits (4 bytes) on 32-bit systems and 64 bits (8 bytes) on 64-bit systems. A kilobyte is 1,024 bytes (not 1,000 — because 2¹⁰ = 1,024 is the convenient binary boundary).

Why is hex used for color codes?

An RGB color has three channels (red, green, blue), each 0–255. In hex, 0–255 maps to 00–FF — exactly two hex digits per channel. So a full color fits in 6 hex digits (#RRGGBB). It's compact, human-readable for developers, and maps directly to the underlying byte structure.