Binary System
Digital electronics ensure that computer systems work with an "on" or "off" state. Voltage levels are often used to indicate whether an electronic system is "on" or "off." If your stereo showed no voltage that would mean it was "off," if on the other hand it did show some voltage, then it would be "on." There are other ways to show whether a digital electronic device was "on or "off."
CDROM's use microscopic dark spots on the surface of the disk to indicate "off" while the ordinary shiny surface shows it is "on." Hard Disk Drives use magnetism, and computer memory uses electric charges stored in capacitors to indicate if the device is "on" or "off."
This "on" and "off" pattern stored in the computer is used to encode numbers using the binary number system. We can use the binary number system to store ordinary numbers, such as 16 or 345. It does this by using the numbers "1" and "0."
A computer sees the number 1 as "on" and the number 0 as "off." Computer circuits can do all sorts of maths; divide, add, multiply and subtract etc by using these binary numbers.
In the decimal system each column is worth 10x more than the previous column. For example; 111 can be written as 1x100+1x10+1x1 in expanded notation form. 3456 = 3x1000+4x100+5x10+6x1. It is easy to see that when you start with the right hand column each column to the left is worth ten times more. The ones, tens, hundreds and thousands columns.
The binary number system is easy to follow as well. However with the binary system each column is worth twice the value of the column before. In the binary number system the columns are worth: 1, 2, 4, 8, 16, 32, 64, 128, etc.
What does the root word "bi" mean? Look it up in the dictionary. Do you know any other words that start with "bi" that have anything to do with the number 2? I can think of bicycle and bipedal. Can you think of any more?
| Decimal Place Value |
|---|
| 10 000 | 1 000 | 100 | 10 | 1 |
In the decimal place value chart you start at the right hand side and multiply each column by 10.
| Binary Place Value |
|---|
| 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
As you can see in the binary place value chart you also start at the right hand side however with each column you just double the number. Double 1 gives you 2, double 2 gives you 4, double 4 gives you 8 and so on.
If you have a printer available then click on this link to the Light Bulb Binary game and print it out. If you don't have a printer available, then you've got some hard work ahead of you - go write it out!
You will need a pair of scissors on hand to cut out your place chart and the light bulbs.
This is how we play the game. Place all your lightbulbs on the chart with the "off" side showing.
If we wanted to represent the number 2 we would turn over the light bulb that is on the number 2 column. This light bulb will now be "on."
If we wanted to represent the number 5 we would have to turn over the light bulbs that are on 4 and 1, as 4+1=5. Get it?
How about the number 11?
The light bulbs read "on, off, on" or 101 ("one zero one").
Try other numbers - 28, 15, 36, 7. Work with another person and quiz each other.
What happens when you want to show a 38 or a 61 or 103? (Add extra columns to your place value chart).
Cisco Binary Game
This is a great game I found on the Cisco site. Have fun trying to keep up with working out the binary numbers. Cisco Binary Game
NB: I acknowledge that I found this info on the internet, can't remember which site, but the info is great and I use it all the time with my students. If I ever find that site again, i'll put a link to it. :)
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