ASCII - “American Standard Code for Information Interchange” encoding of characters. Binary - A notation that utilizes only two options for each selection. Bit - Short for “Binary Digit”. It is one digit’s location in a binary number. Code/Coding - Transformation from one representation to another. Coding tools suitable for a range of middle school students. Explore this Best Coding Tools for Middle School Top Picks list of 38 tools curated by Common Sense Education editors to find relevant and engaging edtech solutions for your classroom. Code games or fun displays with mini piece of hardware. Activities, and a gallery, is free. 8 Super-Easy and Crazy-FUN Coding Activities for Kids. Cubetto: The Coding Robot Toy – First, let me tell you about the new coding toy that inspired our coding adventures.Cubetto is a screenless coding toy ideal for preschoolers, ages 3 to 6. However, all three of my kids love it and they are ages 6, 9, and 11.
What is it?
The binary number system is a base-2 number system. This means it only has two numbers: 0 and 1. All information in a computer (words, pictures, movies, sound) is stored and transmitted as sequences of bits, or binary digits.
A bit is a single piece of data which can be thought of as either zero or one. Each binary number is made up of bits, for example, the number 1010 is made of 4 bits. When you have 8 bits altogether, this is known as a byte. A byte may look like the number 01000100 and in this case represents the letter 'D'.
Australian Curriculum definition
Binary
A use of two states or permissible values to represent data, such as ON and OFF positions of a light switch or transistors in a computer silicon chip that can be in either the electrical state of ON or OFF.
Binary data are typically represented as a series of single digits referred to as binary digits (or bits) due to each taking on the value of either 0 or 1. The image below shows how a dashed line might be represented in binary.
Source: Australian Curriculum: Technologies glossary
A Binary Number is made up of only 0s and 1s.
| Example of a Binary Number |
There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary!
A 'bit' is a single binary digit. The number above has 6 bits.
Binary numbers have many uses in mathematics and beyond.
In fact the digital world uses binary digits.
How do we Count using Binary?
It is just like counting in decimal except we reach 10 much sooner.
| Binary | |
| 0 | We start at 0 |
| 1 | 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 | ||
The same thing is done in binary ...
| Binary | ||
| 0 | Start at 0 | |
| • | 1 | Then 1 |
| •• | 10 | Now start back at 0 again, but add 1 on the left |
| ••• | 11 | 1 more |
| •••• | ??? | But NOW what ... ? |
| What happens in Decimal? | |||
| 99 | When we run out of digits, we ... | ||
| 100 | ... start back at 0 again, but add 1 on the left | ||
And that is what we do in binary ...
| Binary | ||
| 0 | Start at 0 | |
| • | 1 | Then 1 |
| •• | 10 | Start back at 0 again, but add 1 on the left |
| ••• | 11 | |
| •••• | 100 | start back at 0 again, and add one to the number on the left... ... but that number is already at 1 so it also goes back to 0 ... ... and 1 is added to the next position on the left |
| ••••• | 101 | |
| •••••• | 110 | |
| ••••••• | 111 | |
| •••••••• | 1000 | Start back at 0 again (for all 3 digits), add 1 on the left |
| ••••••••• | 1001 | And so on! |
See how it is done in this little demonstration (press play button):
Decimal vs Binary
Here are some equivalent values:
| Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Binary: | 0 | 1 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |
Symmetry
Binary numbers also have a beautiful and elegant pattern:
Here are some larger values:
| Decimal: | 20 | 25 | 30 | 40 | 50 | 100 | 200 | 500 |
|---|---|---|---|---|---|---|---|---|
| Binary: | 10100 | 11001 | 11110 | 101000 | 110010 | 1100100 | 11001000 | 111110100 |
'Binary is as easy as 1, 10, 11.'
Now see how to use Binary to count past 1,000 on your fingers:
Position
In the Decimal System there are Ones, Tens, Hundreds, etc
In Binary there are Ones, Twos, Fours, etc, like this:
This is 1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8)
= 13.625 in Decimal
Numbers can be placed to the left or right of the point, to show values greater than one and less than one.
| 10.1 | |
| The number to the left of the point is a whole number (such as 10) | |
| As we move further left, every number place gets 2 times bigger. | |
| The first digit on the right means halves (1/2). | |
| As we move further right, every number place gets 2 times smaller (half as big). | |
Example: 10.1
- The '10' means 2 in decimal,
- The '.1' means half,
- So '10.1' in binary is 2.5 in decimal
You can do conversions at Binary to Decimal to Hexadecimal Converter.
Words
The word binary comes from 'Bi-' meaning two. We see 'bi-' in words such as 'bicycle' (two wheels) or 'binocular' (two eyes).
| When you say a binary number, pronounce each digit (example, the binary number '101' is spoken as 'one zero one', or sometimes 'one-oh-one'). This way people don't get confused with the decimal number. |
A single binary digit (like '0' or '1') is called a 'bit'.
For example 11010 is five bits long.
The word bit is made up from the words 'binary digit'
How to Show that a Number is Binary
To show that a number is a binary number, follow it with a little 2 like this: 1012
This way people won't think it is the decimal number '101' (one hundred and one).
Examples
Example: What is 11112 in Decimal?
- The '1' on the left is in the '2×2×2' position, so that means 1×2×2×2 (=8)
- The next '1' is in the '2×2' position, so that means 1×2×2 (=4)
- The next '1' is in the '2' position, so that means 1×2 (=2)
- The last '1' is in the ones position, so that means 1
- Answer: 1111 = 8+4+2+1 = 15 in Decimal
Example: What is 10012 in Decimal?
- The '1' on the left is in the '2×2×2' position, so that means 1×2×2×2 (=8)
- The '0' is in the '2×2' position, so that means 0×2×2 (=0)
- The next '0' is in the '2' position, so that means 0×2 (=0)
- The last '1' is in the ones position, so that means 1
- Answer: 1001 = 8+0+0+1 = 9 in Decimal
Example: What is 1.12 in Decimal?
- The '1' on the left side iaas in the ones position, so that means 1.
- The 1 on the right side is in the 'halves' position, so that means 1×(1/2)
- So, 1.1 is '1 and 1 half' = 1.5 in Decimal
Example: What is 10.112 in Decimal?
- The '1' is in the '2' position, so that means 1×2 (=2)
- The '0' is in the ones position, so that means 0
- The '1' on the right of the point is in the 'halves' position, so that means 1×(1/2)
- The last '1' on the right side is in the 'quarters' position, so that means 1×(1/4)
- So, 10.11 is 2+0+1/2+1/4 = 2.75 in Decimal
Free Fun Binary Code Activities Middle School
'There are 10 kinds of people in the world,
those who understand binary numbers, and those who don't.'