> For the complete documentation index, see [llms.txt](https://alham-rizvi.gitbook.io/alhamrizvi/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://alham-rizvi.gitbook.io/alhamrizvi/cryptography/hashing/24.-hex.md).

# Hexadecimal (Hex) Encoding

## What is Hex?

**Hexadecimal** is a base-16 number system using digits `0–9` and letters `A–F` (case-insensitive). It is widely used in cryptography and computing to represent binary data in a human-readable format.

```
Base-2  (Binary):      11111111
Base-10 (Decimal):     255
Base-16 (Hex):         FF
```

***

## Hex Alphabet

| Decimal | Hex | Binary |
| ------- | --- | ------ |
| 0       | 0   | 0000   |
| 1       | 1   | 0001   |
| 2       | 2   | 0010   |
| 3       | 3   | 0011   |
| 4       | 4   | 0100   |
| 5       | 5   | 0101   |
| 6       | 6   | 0110   |
| 7       | 7   | 0111   |
| 8       | 8   | 1000   |
| 9       | 9   | 1001   |
| 10      | A   | 1010   |
| 11      | B   | 1011   |
| 12      | C   | 1100   |
| 13      | D   | 1101   |
| 14      | E   | 1110   |
| 15      | F   | 1111   |

***

## How Hex Encoding Works

Each byte (8 bits) maps to **exactly 2 hex characters**:

```
Byte:  0x4A  =  0100 1010
Hex:   4     A
       ↑     ↑
    upper   lower
    nibble  nibble
```

### Example: "Hello" in Hex

```
H  →  72  →  48
e  →  101 →  65
l  →  108 →  6C
l  →  108 →  6C
o  →  111 →  6F

"Hello" = 48 65 6C 6C 6F
```

***

## Hex in Cryptography

* **Hash outputs**: MD5 = 32 hex chars, SHA-256 = 64 hex chars, SHA-512 = 128 hex chars
* **Keys**: AES-256 key = 64 hex chars (32 bytes)
* **Nonces/IVs**: displayed as hex
* **Memory addresses**: shown in hex (0x7fff5fc...)
* **Color codes in web**: #FF5733

***

## Implementation Examples

### Python

```python
# Bytes to hex
data = b"Hello"
hex_str = data.hex()
print(hex_str)  # 48656c6c6f

# With spaces (visual grouping)
hex_spaced = ' '.join(f'{b:02x}' for b in data)
print(hex_spaced)  # 48 65 6c 6c 6f

# Hex to bytes
decoded = bytes.fromhex("48656c6c6f")
print(decoded)  # b'Hello'

# Using binascii
import binascii
hex_str = binascii.hexlify(b"Hello").decode()
original = binascii.unhexlify(hex_str)

# Integer to hex
print(hex(255))     # '0xff'
print(f"{255:02x}") # 'ff'
print(f"{255:08x}") # '000000ff' (padded to 8 chars)
```

### JavaScript

```javascript
// String to hex
function strToHex(str) {
    return Array.from(str)
        .map(c => c.charCodeAt(0).toString(16).padStart(2, '0'))
        .join('');
}
console.log(strToHex("Hello")); // 48656c6c6f

// Hex to string
function hexToStr(hex) {
    return hex.match(/.{2}/g)
        .map(byte => String.fromCharCode(parseInt(byte, 16)))
        .join('');
}

// Buffer to hex (Node.js)
const buf = Buffer.from("Hello");
console.log(buf.toString('hex')); // 48656c6c6f

// Hex to Buffer
const restored = Buffer.from("48656c6c6f", 'hex');
```

### Go

```go
import "encoding/hex"

// Encode
encoded := hex.EncodeToString([]byte("Hello"))
// "48656c6c6f"

// Decode
decoded, err := hex.DecodeString("48656c6c6f")
// []byte("Hello")
```

### Rust

```rust
// Using hex crate
let encoded = hex::encode(b"Hello");  // "48656c6c6f"
let decoded = hex::decode("48656c6c6f").unwrap();
```

***

## Hex vs Base64 Comparison

| Property       | Hex                     | Base64                 |
| -------------- | ----------------------- | ---------------------- |
| Alphabet size  | 16 chars                | 64 chars               |
| Size expansion | 2× original             | 1.33× original         |
| Readability    | High (each byte clear)  | Lower                  |
| Use case       | Debugging, hashes, keys | Data transfer, storage |
| Characters     | 0-9, a-f                | A-Z, a-z, 0-9, +, /    |

***

## Size Examples

| Data         | Bytes | Hex chars | Base64 chars |
| ------------ | ----- | --------- | ------------ |
| MD5 hash     | 16    | 32        | 24           |
| SHA-1 hash   | 20    | 40        | 28           |
| SHA-256 hash | 32    | 64        | 44           |
| SHA-512 hash | 64    | 128       | 88           |
| AES-128 key  | 16    | 32        | 24           |
| AES-256 key  | 32    | 64        | 44           |

***

## Common Hex Prefixes

| Prefix | Language/Context            |
| ------ | --------------------------- |
| `0x`   | C, Python, JavaScript, Rust |
| `#`    | CSS colors                  |
| `\x`   | Escape sequences in strings |
| `U+`   | Unicode code points         |
| `%`    | URL encoding                |

***

## Best Practices

* Use **lowercase hex** for consistency (`a-f` not `A-F`)
* Always **zero-pad** to fixed length (`02x` format)
* Use built-in library functions — don't roll your own hex encoder
* For display, add **spaces or colons** between bytes for readability: `48:65:6c:6c:6f`
* When comparing hashes, always **compare bytes** not hex strings (avoid timing attacks)


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