Hexadecimal

Last updated on 2025-10-30 | Edit this page

Estimated time: 5 minutes

Overview

Questions

  • What is hexadecimal?
  • Why is it important?
  • What are the basics of hexadecimal we need to understand?

Objectives

  • Learn what hexadecimal is.
  • Learn how to construct a hexadecimal sequence with arbitrary meaning.

Introduction to hexadecimal

  • Hexadecimal is a way of representing numbers.
  • Just as decimal is Base10, hexadecimal is just Base16.
      
DEC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HEX 0 1 2 3 4 5 6 7 8 9 A B C D E F
DEX 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
HEX 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F


  • While you can learn to convert decimal to hexadecimal, you are more likely to convert hexadecimal to decimal.
0x00 = (16 x 0 = 0) + (1 x 0 = 1) = 0
0x01 = (16 x 0 = 0) + (1 x 1 = 1) = 1
0x0A = (16 x 0 = 0) + (1 x 10 = 10) = 10
0xFF = (16 x 15 = 240) + (1 x 15 = 15) = 255


Challenge

Try it in your search engine

If you use a search engine, what results do you get for the following queries?

  • 0xFF in decimal
  • 42 in hexadecimal
  • 82 in binary
  • 0b1100 in decimal

Search engines can conveniently do the work of converting from decimal to hexadecimal and back for you. You can also investigate binary numbers quickly and easily this way without having to work out the layout of bits.

Callout

Zero to hero!

Zero is an important number in computer science and we will see it often when we analyse digital records.

Callout

What does 0x mean?

We use the 0x prefix to signify hexadecimal. When we document hex sequences like above 0xE4 0xB8 0x96 is also equivalent to 0xE4B896. How you choose write this information depends on context.

You also saw 0b as a prefix. This is used to denote binary (base2),

e.g. 0b1100 equals 0x0C equals 12.

  • A single hexadecimal number is a convenient representation of 1-byte, i.e. 8 bits of binary which is the smallest and most convenient unit of data used in computer memory.
Callout

Binary

We won’t go into binary here, but if you ever want to look at the binary representation of a number, modern search engines can do the conversion for you if you ask: 255 in binary (just as you can ask: 255 in hexadecimal.

  • 0 (b00000000) is the smallest number you can represent in binary in a single byte,
  • 255 (b11111111) is the largest possible value.

ASCII table

  • That might feel like a lot, but before we have to convert numbers every which way, we have another tool at our disposal, a lookup table which is still relevant in our research.

  • In the lookup table below (the ASCII table) you can see how bytes take on more meaning to a computer, e.g. as control symbols, punctuation symbols, numbers, and letters.

  • For the numbers and letters, this is just one encoding. We will talk about the importance of that below but first let’s look at the table for a second.

Discussion

question

When you look at the table, think about your favorite (decimal) number.

  • What symbol does it represent?
  • What’s your favourite (hexadecimal) number, what symbol does it represent?


ASCII table

Dec Hex Char Dec Hex Char Dec Hex Char Dec Hex Char Dec Hex Char
0 0 NUL 25 19 EM 51 33 3 77 4D M 103 67 g
1 1 SOH 26 1A SUB 52 34 4 78 4E N 104 68 h
2 2 STX 27 1B ESC 53 35 5 79 4F O 105 69 i
3 3 ETX 28 1C FS 54 36 6 80 50 P 106 6A j
4 4 EOT 29 1D GS 55 37 7 81 51 Q 107 6B k
5 5 ENQ 30 1E RS 56 38 8 82 52 R 108 6C l
6 6 ACK 31 1F US 57 39 9 83 53 S 109 6D m
7 7 BEL 32 20 space 58 3A : 84 54 T 110 6E n
8 8 BS 33 21 ! 59 3B ; 85 55 U 111 6F o
9 9 HT 34 22 ” 60 3C < 86 56 V 112 70 p
10 0A LF 35 23 # 61 3D = 87 57 W 113 71 q
11 0B VT 36 24 $ 62 3E > 88 58 X 114 72 r
12 0C FF 37 25 % 63 3F ? 89 59 Y 115 73 s
13 0D CR 38 26 & 64 40 @ 90 5A Z 116 74 t
14 0E SO 39 27 65 41 A 91 5B [ 117 75 u
15 0F SI 40 28 ( 66 42 B 92 5C \ 118 76 v
16 10 DLE 41 29 ) 67 43 C 93 5D ] 119 77 w
17 11 DC1 42 2A * 68 44 D 94 5E ^ 120 78 x
18 12 DC2 43 2B + 69 45 E 95 5F _ 121 79 y
19 13 DC3 44 2C , 70 46 F 96 60 ` 122 7A z
20 14 DC4 45 2D - 71 47 G 97 61 a 123 7B {
21 15 NAK 46 2E . 72 48 H 98 62 b 124 7C
22 16 SYN 47 2F / 73 49 I 99 63 c 125 7D }
23 17 ETB 48 30 0 74 4A J 100 64 d 126 7E ~
24 18 CAN 49 31 1 75 4B K 101 65 e 127 7F DEL
50 32 76 4C L 102 66 f

Encodings

  • In a file format, they translate to some information that a computer can understand, e.g. numbers 0x30 to 0x39 are (universally) the numbers 0 - 9.
  • In the olden days software devs only thought about english, and so character encodings started life there, and then became more inclusive – today we have unicode
  • Looking at files from the early days can be tricky when doing digital forensics but file format signature development asks two things:
  1. That we understand the samples we have are the same format.
  2. That we can find patterns in these files, even if we don’t always know what those patterns mean.


Example Māori macrons in UTF-8


0xC4 0x81 = ā

0xC4 0x93 = ē

0xC4 0xAB = ī

0xC5 0x8D = ō

0xC5 0xAB = ū

0xC4 0x80 = Ā

0xC4 0x92 = Ē

0xC4 0xAA = Ī

0xC5 0x8C = Ō

0xC5 0xAA = Ū


World in Japanese in UTF-8


0xE3 0x81 0x93 = こ

0xE3 0x82 0x93 = ん

0xE3 0x81 0xAB = に

0xE3 0x81 0xA1 = ち

0xE3 0x81 0xAF = は

0xE4 0xB8 0x96 = 世

0xE7 0x95 0x8C = 界

Famous Byte sequences

  • D0CF11E0
  • II
  • MM
  • GIF89a
  • PK

You can ask the room if they know what these byte sequences might be.

  • Microsoft Office
  • TIFF
  • Also TIFF!
  • GIF
  • ZIP
Callout

Magic numbers: your first file format signatures

You will begin to recognize these sequences in your file format research!

Putting it together

Can you use the ASCII table above to construct a byte-sequence?

Challenge

Challenge

Write down the hexadecimal sequence for “Hello world”.

48 65 6C 6C 6F 20 77 6F 72 6C 64


Key Points
  • Hexadecimal is a number system.
  • Hexadecimal makes it easier to understand “binary”.
  • Hexadecimal is mapped to signals and characters that have meaning to a computer.
  • Hexadecimal can take on arbitrary meaning through “encodings”.
  • Hexadecimal is the foundation for a PRONOM signature!