What Is Hexadecimal?

The short answer

Hexadecimal is a way of writing numbers using sixteen symbols instead of ten. It runs 0 to 9 as you would expect, then continues A, B, C, D, E, F for the values ten to fifteen.

It is a notation, not a different kind of number. FF and 255 are the same quantity written two ways, exactly as "twelve" and "XII" are.

What a base actually is

A base is how many symbols you have before you run out and start a new column. Decimal has ten, so after 9 comes 10 — one group of ten, no units left over. Hexadecimal has sixteen, so counting continues past 9 with letters, and only rolls over after F.

decimal   0 1 2 3 4 5 6 7 8 9 10 11 12 ...
                                 ↑
                          rolls over after 9

hex       0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 ...
                                           ↑
                                    rolls over after F

The 10 in the second row is sixteen, not ten. This is the single most common source of confusion, and it disappears once you read 10 as "one group of the base" rather than as the word "ten".

Why letters

Base 16 needs sixteen distinct single symbols. The decimal system supplies only ten, so six more had to come from somewhere, and the first six letters were the obvious choice — already ordered, already on every keyboard, unambiguous next to digits.

How place value works

Each position is worth sixteen times the one to its right, in exactly the way each decimal position is worth ten times the one to its right. The number system guide goes further into counting, arithmetic and signed values.

2A7 in hex

  2 in the 256s place  →  2 × 256 = 512
  A in the 16s place   → 10 ×  16 = 160
  7 in the 1s place    →  7 ×   1 =   7
                                    -----
                                      679

Why computers use it

Computers store everything in bits. Bits are unreadable in bulk and decimal hides their structure, so a middle notation is needed — and hex is the one that fits exactly.

Sixteen is 2⁴, so one hex digit holds exactly four bits with nothing left over. A byte is always two hex digits. A 32-bit value is always eight. No other convenient base lines up that cleanly with binary.

Where you meet it

• Color codes. #1A73E8 is three bytes: red, green, blue.
• Memory addresses. Debuggers and crash logs show addresses in hex because byte boundaries stay visible.
• MAC addresses. Six bytes identifying a network interface.
• Hashes and checksums. An MD5 is 32 hex characters, a SHA-256 is 64.
• Character codes. Unicode code points are written as U+00E9.
• Error codes. Windows and firmware errors are routinely given in hex.
• File signatures. A PNG always begins 89 50 4E 47.

Reading hex without converting it

Three habits make hex readable at a glance, without arithmetic.

1. Count the digits. Two is a byte, four is a word, eight is 32 bits, thirty-two is a UUID or MD5, sixty-four is SHA-256.
2. Read the first digit as a fraction of sixteen. C something is about three quarters of the way up, 8 something is about half.
3. Recognise the landmarks. 00 is empty, FF is full, 80 is the sign bit, 7F is the top of ASCII.

Try it yourself

The hex converter shows every base at once and breaks your input into nibbles, so you can watch the digit-to-bit mapping directly. For the arithmetic behind each direction, see converting hex to decimal by hand.

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