Number bases
Quick links 
Number bases 
Converting number bases 
Units of information 
Binary arithmetic 
Character encoding 
Representing images 
Representing sound 
Data compression 
Syllabus content
Content  Additional Information  

Understand the following number bases:


Understand that computers use binary to represent all data and instructions.  Students should be familiar with the idea that a bit pattern could represent different types of data including text, image, sound and integer.  
Explain why hexadecimal is often used in computer science. 
Number bases
Number bases
We usually use Arabic numbers, which are base 10, or decimal. Computers use binary, which is base 2. This page deals with numbers in other bases. Enter a number to convert it to a different base, or count in a base.
How numbers in other bases work
In Arabic numbers (decimal, or base 10), there are 10 digits: 0,1,2,3,4,5,6,7,8,9. You need one digit each to count up to 9, but two digits for ten, and three digits for a hundred, which is ten times ten. In Binary, base 2, you need two digits for two, as you only have two digits, 0 and 1. Base 5 has five digits, and the number five becomes 10. For base 16, you will need sixteen digits, and there are only ten numerals. So we use the letters A,B,C,D,E,F. These represent the decimal numbers 10, 11, 12, 13, 14 and 15. Look at the table below and find the pattern for these bases.
Base 10  Base 2  Base 3  Base 4  Base 5  Base 8  Base 16 

1  1  1  1  1  1  1 
2  10  2  2  2  2  2 
3  11  10  3  3  3  3 
4  100  11  10  4  4  4 
5  101  12  11  10  5  5 
6  110  20  12  11  6  6 
7  111  21  13  12  7  7 
8  1000  22  20  13  10  8 
9  1001  100  21  14  11  9 
10  1010  101  22  20  12  A 
11  1011  102  23  21  13  B 
12  1100  110  30  22  14  C 
13  1101  111  31  23  15  D 
14  1110  112  32  24  16  E 
15  1111  120  33  30  17  F 
16  10000  121  100  31  20  10 
17  10001  122  101  32  21  11 
18  10010  200  102  33  22  12 
19  10011  201  103  34  23  13 
20  10100  202  110  40  24  14 
Base systems like binary and hexadecimal seem a bit strange at first. The key is understanding how different systems “tick over” like an odometer when they are full. Base 10, our decimal system, “ticks over” when it gets 10 items, creating a new digit. We wait 60 seconds before “ticking over” to a new minute. Hex and binary are similar, but tick over every 16 and 2 items, respectively.
3.1 Fundamentals of algorithms
 3.1.1 Representing algorithms
 3.1.2 Efficiency of algorithms
 3.1.3 Searching algorithms
 3.1.4 Sorting algorithms
3.2 Programming
 3.2.1 Data types
 3.2.2 Programming concepts
 3.2.3 Arithmetic operations in a programming language
 3.2.4 Relational operations in a programming language
 3.2.5 Boolean operations in a programming language
 3.2.6 Data structures
 3.2.7 Input/output and file handling
 3.2.8 String handling operations in a programming language
 3.2.9 Random number generation in a programming language
 3.2.10 Subroutines (procedures and functions)
 3.2.11 Structured programming
 3.2.12 Robust and secure programming
 3.2.13 Classification of programming languages
3.3 Fundamentals of data representation
 3.3.1 Number bases
 3.3.2 Converting between number bases
 3.3.3 Units of information
 3.3.4 Binary arithmetic
 3.3.5 Character encoding
 3.3.6 Representing images
 3.3.7 Representing sound
 3.3.8 Data compression
3.4 Computer systems
 3.4.1 Hardware and software
 3.4.1 Operating systems
 3.4.2 Boolean logic
 3.4.3 Software classification
 3.4.4 Systems architecture
3.5 Fundamentals of computer networks
3.6 Fundamentals of cyber security
3.7 Ethical, legal and environmental impacts of digital technology on wider society, including issues of privacy
 3.7.1 Ethical impacts of digital technology on wider society
 3.7.2 Legal impacts of digital technology on wider society
 3.7.3 Environmental impacts of digital technology on wider society
 3.7.4 Issues of privacy