# 🔢 How Binary Is Represented by Hexadecimal Hexadecimal (or "hex") is a compact way to represent binary numbers using **base-16 digits**. It’s especially useful when working with binary data like the 32-bit codes in the Universal Hex Taxonomy (UHT). --- ## 🧮 The Basics - **Binary** is base-2: uses only `0` and `1` - **Hexadecimal** is base-16: uses digits `0–9` and letters `A–F` | Decimal | Binary | Hex | |---------|--------|-----| | 0 | 0000 | 0 | | 1 | 0001 | 1 | | 2 | 0010 | 2 | | 3 | 0011 | 3 | | 4 | 0100 | 4 | | 5 | 0101 | 5 | | 6 | 0110 | 6 | | 7 | 0111 | 7 | | 8 | 1000 | 8 | | 9 | 1001 | 9 | | 10 | 1010 | A | | 11 | 1011 | B | | 12 | 1100 | C | | 13 | 1101 | D | | 14 | 1110 | E | | 15 | 1111 | F | --- ## 🔗 4 Bits per Hex Digit Every **4 binary digits (bits)** make **1 hex digit**. **Example:** Binary: 10111111 Split:  1011 1111 Hex:    B    F So `10111111` in binary = `BF` in hex. --- ## 📦 UHT Code Example UHT codes are **32 bits**, grouped into **4 sections of 8 bits**: - Physical traits: bits 1–8 - Functional traits: bits 9–16 - Abstract traits: bits 17–24 - Social traits: bits 25–32 **Example:** Binary: 11010111 10001000 00000000 11000101 Hex:    D7        88        00        C5 UHT Code: D78800C5 --- ## ✅ Why Use Hex? - Easier to read than long binary strings - Every hex digit = exactly 4 bits - Widely used in digital systems - Essential for compact encoding in systems like UHT