Hexadecimal

Problem

A tool shows C3 BC, a document mentions U+00FC, and a configuration contains 0xFF. What do these values mean? You need to read byte values and understand their context without doing every conversion by hand.

Solution

1. Hexadecimal is a way to write numbers

Decimal uses ten digits: 0–9. Hexadecimal, often shortened to hex, uses sixteen: 0–9 and A–F. The six letters stand for these values:

A → 10
B → 11
C → 12
D → 13
E → 14
F → 15

This is the convention for hexadecimal notation. There is no G. Uppercase and lowercase mean the same thing: FC and fc represent the same number.

2. Why the next position counts groups of 16

In decimal, a single digit runs out after 9, so the next number is 10: one group of ten and zero left over. In hexadecimal, a single digit runs out after F, so the next number is also written 10. Here it means one group of sixteen and zero left over.

Decimal 14 → hex E
Decimal 15 → hex F
Decimal 16 → hex 10
Decimal 17 → hex 11
Decimal 26 → hex 1A
Decimal 27 → hex 1B

Each position is worth sixteen times the position to its right. From right to left, the positions count ones, sixteens, then groups of 256. For two hex digits, multiply the left digit's value by 16 and add the right digit's value:

1A → 1 × 16 + 10 = 26
C3 → 12 × 16 + 3 = 195
BC → 11 × 16 + 12 = 188
FF → 15 × 16 + 15 = 255

3. Two hex digits represent one byte

A bit is a 0 or a 1. A byte contains eight bits, giving 256 possible bit patterns. Interpreted as an unsigned number, a byte holds a value from 0 to 255. A single hex digit represents four bits. Two hex digits therefore represent one complete byte:

C  → 1100
3  → 0011
C3 → 11000011 → one byte

The number 195 in decimal, C3 in hexadecimal, and 11000011 in binary all describe the same value. You can convert hex directly to binary one digit at a time; going through decimal is optional. 00 is the smallest unsigned byte value, and FF is the largest. Two raw bytes displayed as C3 BC contain sixteen bits in total.

4. Why hexadecimal is useful

Compare two ways of displaying the same two bytes:

Binary → 11000011 10111100
Hex    → C3       BC

Hex is shorter and easier to compare or copy. Every pair of digits still corresponds neatly to one byte. Tools often show bytes this way when you inspect files, network messages, or memory. You also encounter hex in IPv6 addresses, MAC addresses, hashes, and color values. For example, the color #FF0000 uses FF for red, 00 for green, and 00 for blue.

5. Recognize the notation and its context

0xFF means the hexadecimal number FF, or decimal 255. The prefix 0x tells you which number system is being used. U+00FC means a Unicode code point whose number is written in hex. It identifies the character ü. Leading zeros do not change that numeric value: FC and 00FC both mean 252. Spaces in a byte display such as C3 BC separate bytes for readability. A sequence of 32 hex digits can represent 16 raw bytes. The surrounding format determines how to interpret those bytes: as text, a number, a color, or something else.

Core idea: hexadecimal is a readable way to write numeric and byte values. Two hex digits represent one byte; the surrounding format determines what those bytes mean.