Hexadecimal

Last updated on 2026-09-21 | Edit this page

Overview

Questions

  • What is hexadecimal?
  • What are the basics of hexadecimal?
  • Why is hexadecimal important to look at files?

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.
  • Hexadecimal uses 16 symbols (0-9 and A-F) compared to the 10 symbols (0-9) familiar in the decimal number system.
  • Just as decimal is otherwerise known as 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
DEC 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 when looking at file formats.
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 pair of hexadecimal numbers 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

  • Binary uses 2 symbols, 0 and 1.
  • Binary can otherwise be referred to as Base2. We won’t explore binary in detail 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.

ASCII lookup 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

Magic Numbers

To do file format research we look at the structure of the files in hex

  • Files have reoccurring byte patterns within them that show us what they are
  • Computers read bytes to render on your screen in a similar way to how we might read a letter. A pre-known structure that helps disseminate the information.


a handwritten letter annotated to show the page number, addressee, main message, sender and sign-off
How humans read a file


a photograph of a pig, showing its contents as hexadecimal and decoded text. image of a blue arrow pointing rightwards the same image file of a pig shown as hexadecimal, annotated to show the magic bytes, the image header and the pixel specifications
How computers read a file

Famous Byte sequences

  • D0CF11E0
  • II
  • MM
  • GIF89a
  • PK These are all ‘Magic Numbers’ - sequences that the format developers have chosen for quick identification of their file formats.
  • 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!