Hexadecimal

Hexadecimal (“hex”) is a way of writing numbers with sixteen digits instead of ten.

You’ll see it everywhere in Pearl. Every key, hash, signature and raw transaction on this site is written in hex. That’s not because the numbers are special. It’s because hex is the tidiest way to write down bytes.

Try it

Type a number in any box. Watch it change between decimal, hex and binary.

What are the sixteen digits?

Normal counting (decimal) has ten digits, 0 to 9. When you run out, you carry one into the next column: 9, then 10.

Hex has six more digits before it carries. It borrows letters for them:

So in hex, “10” means sixteen, not ten. To avoid confusion, hex numbers are often written with a 0x in front: 0x10 is sixteen.

Capital and small letters mean the same thing. Pearl’s software prints small letters.

Why does every byte take two characters?

Because sixteen is a power of two.

One hex digit has 16 possible values, which is exactly what four bits can hold (2 × 2 × 2 × 2 = 16). Half a byte, four bits, is sometimes called a nibble. Two nibbles make a byte, so one byte is always exactly two hex characters, from 00 to ff.

This is the whole reason hex is used. Binary is too long to read (a hash is 256 ones and zeros). Decimal hides where one byte ends and the next begins. Hex is short and keeps the bytes visible: every pair of characters is one byte.

How do you convert hex to decimal?

Each column is worth sixteen times the one to its right, just as each decimal column is worth ten times more.

For a longer number, keep going with 256, 4,096, 65,536 and so on. Pearl’s coin type, the number in every wallet’s derivation path, is 808,276. In hex it is 0xc5554:

Where do you see hex in Pearl?

Almost everywhere data is shown rather than spoken:

• Hashes. A block hash like 3fc851763893a0135ea756d5dcbe355f375e613957930e7f401fafc8ee5533ae is 32 bytes, so 64 characters.
• Raw data. A 108-byte Pearl header is 216 hex characters. A raw transaction is its bytes in hex, start to finish.
• Keys and signatures. A private key is 64 characters, an x-only public key 64, a Schnorr signature 128.
• Constants in the code. Pearl’s difficulty-1 bits are 0x1b00ffff, the XMSS opcode is 0xde, and the mainnet network magic is 0x50524C4D, which spells “PRLM” in ASCII.

How do you find one byte in a long hex string?

Count in pairs. Byte number n (counting from 0) starts at character 2n, and every field is twice as many characters as it is bytes.

Take block 130,825’s header, 216 characters long. Its bits field is bytes 72 to 75, so it sits at characters 144 to 151: ebd06a17. Its Merkle root is bytes 36 to 67, characters 72 to 135.

Pearl’s code, explorers and this site always give offsets in bytes, not characters. When a page says “offset 76”, double it to find the spot in the hex.

Is hex a different kind of number?

No. Hex is only a way of writing a number, like Roman numerals. 0xc2, 194 and 11000010 are the same value, stored as the same eight bits.

That matters when you hash things. Hashing the text “c2” (two characters, two bytes) is not the same as hashing the byte 0xc2 (one byte). Tools on this site always say which one they mean.

// String returns the Hash as the hexadecimal string of the byte-reversed
// hash.
func (hash Hash) String() string {
	for i := 0; i < HashSize/2; i++ {
		hash[i], hash[HashSize-1-i] = hash[HashSize-1-i], hash[i]
	}
	return hex.EncodeToString(hash[:])
}

(194).toString(16);          // 'c2'
parseInt('c5554', 16);       // 808276
const hex = (bytes) => [...bytes].map((b) => b.toString(16).padStart(2, '0')).join('');