Adding binary numbers
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 |
Task
Using pen and paper or a notepad on your computer, write out the above sequence.
Continue the sequence up to the equivalent of the decimal number 32.
Compare your answer with a classmate. Do you get the same answer?
Binary data is often grouped together in 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
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
Click on the Exercises tab and complete as many as you can.
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...
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