First let’s review how the decimal system works


A Binary Number is made up of only 0s and 1s, for instance


A “bit” is a single binary digit. The number above has 6 bits.

There are no other digits (2, 3, 4, 5, 6, 7, 8 or 9) in Binary



How do we Count using Binary?

We start at 0
Then 1
But then there is no symbol for 2 … what do we do?

Well how do we count in Decimal?
0 Start at 0
… Count 1,2,3,4,5,6,7,8, and then…
9 This is the last digit in Decimal
10 So we start back at 0 again, but add 1 on the left

99 When we run out of digits, we …
100 … start back at 0 again, but add 1 on the left

A similar kind of thing is done in binary …


So each bit has it’s own value, like this:

And we can count like this:

here are some examples


Count binary on your fingers



Coding exercises

 Course 4. Stage 18. Being an artist with binary numbers.



The hexadecimal numeral system, hex, is a numeral system made up of 16 symbols – we’ll learn about it here: Hexadecimal number system

External resources

 Introduction to binary numbers (KaiserScience)

 Intro to computer science: Binary decoder key. Studio.Code.Org

Binary numbers http://csunplugged.org/wp-content/uploads/2014/12/unplugged-01-binary_numbers.pdf

 Treasure Hunt – Finite-State Automata. follows a set of instructions to see if the computer will recognise the word or string of symbols

Representing symbols with ASCII code

 Commodore 64 (C64) Users Manual: Chapter 6 Sprite Graphics

Colour by Numbers—Image Representation



Graphics to Binary data Flash app!

Color By Pixel (11 pages)

Class activity: Computer graphics on a binary level



Learning Standards

Massachusetts Digital Literacy and Computer Science (DLCS) Curriculum Framework

6-8.CT.c.1 Demonstrate that numbers can be represented in different base systems (e.g., binary, octal, and hexadecimal) and text can be represented in different ways (e.g., American Standard Code for Information Interchange [ASCII]).

6-8.CT.c.2 Describe how computers store, manipulate, and transfer data types and files (e.g., integers, real numbers, Boolean Operators) in a binary system.

CSTA Computer Science Teachers Association

5.2 Level 2: Computer Science and Community (L2)

14. Examine connections between elements of mathematics and computer science including binary numbers, logic, sets and functions

5.3.B Computer Science Concepts and Practices (CP

7. Discuss the interpretation of binary sequences in a variety of forms (e.g.,
instructions, numbers, text, sound, image).


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