Everything is Binary
The decimal number system has a sequence, starting at 0.
binary also has a sequence. Here is the sequence of binary numbers from 0000 to 1111:
| binary | decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0001 | 1 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
Decimal-to-Binary Review
How good are you at converting binary to decimal and vice versa? Click the converter to play the super exciting binary-decimal converter game!
Text
Binary is used to represent numbers in a way that computers can understand. But what about text? Web pages are full of it!
As you can imagine, computer systems use binary to represent any letter or character on your keyboard.
Here is a text message just for you. It is being represented in binary. Can you find a binary-to-text converter and find out what your computer is trying to say to you!
As you can see, each character is represented by 8 bits of data:
Each character is represented by 8 bits of information. 8 bits of data comprises 1 byte, now the standard unit of memory size in the digital world.
Grouping bits into bytes make them easier to process and manage. The byte is also the standard digital storage unit.
Some general storage sizes of digital files is:
- a plain text email : 2KB
- a 3 minute mp3 file : 3MB
- a 60 minute MP4 documentary: 2GB
Also, 4 bits is referred to as a nibble.
Nibbles are very useful as we will find out later.
Task
Using the ASCII table, write a message in binary to your partner or teacher on a piece of paper. Remember, if you write the message as seperate bytes, it will be a little easier to decode. ie 01101111 01101000 is easier to decode than 0110111101101000
Adding binary numbers
We are going to add 2 bytes together like a computer has to do all the time. To add binary numbers, we need to understand 4 things:
- 0 + 0 = 0 (binary for 0)
- 1 + 0 = 1 (binary for 1)
- 1 + 1 = 10 (binary for 2)
- 1 + 1 + 1 = 11 (binary for 3)
What are the three numbers in decimal? Can you convert them? The decimal sum should also be correct.
Task
Have a go at these binary addition exerices. Compare your solutions with a classmate.
Food For Thought
So, anything can be represented in binary! And we can do binary addition, subtraction, multiplacation and division. I guess computers would have to know how to do all that, too.
Different kind of information are translated into binary and then stored in a specific format eg .mp3, .jpg, .swf so that application software like Adobe Photoshop knows how to process the data. There must be protocols for each format...
Homework
Create 5 binary addition problems and solve them on a seperate piece of paper. Hide your answers and give the questions to your classmate(s). Can they solve your 5 challenges!?
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