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binary irl (in real life)
binary irl (in real life)
Now we know the difference between base-10 (decimal) and base-2 (binary), and we've shown you one way of converting from base-10 (the one we are familiar with) to base-2 using a grid and some counters.
That activity is a good way to engage an entire class of differing abilities. As it is largely an individual or a pair activity, each student can work thru it on their own and come to their conclusions at different times. We talked about some extra for experts activities that you can also use to extend the ones that understand a bit faster.
This is another way you can introduce base-2 in a more interactive fashion.
The dot cards look like dice or dominos. They are created in A2. We would suggest you either print them in the biggest size your printers will do, or draw them out yourself on large cards.
Put them up so that all the kids can see them laid out. I have had children hold them in the front of the class, but it means those children might not be able to take part.
Make sure the dots are in the right order. the card with the most dots should always be furthest to the left.
Now you ask the kids, how can you make only five dots appear. You ask which cards do you have to hide, and which cards do you have to show?
You then explain that any card that is hidden is "off" and therefore a "0" and any card that you can see is "on" and therefore a 1.
So then you say that "5" in "base-10" is "0101" in "base-2"
I find that this way of explaining binary works best when the kids you are teaching have a similar level of numeracy skill across the board. I have run this activity before when you always get one or two kids doing all the answering, and you are then not sure whether the rest are taking it in.
binary addition
binary addition
This activity assumes you already understand the conversion process from base-10 (denary) to base-2 (binary) and that you can do it quickly and accurately,
When you teach your students how to add in the denary system, you will introduce place values and the concept of a 'carry'. As in, when the two denary numbers you are adding together add to more than 10, the 'leftover' needs to be 'carried' to the next place, or column
So, in this example, 43 + 29 = 72. But actually, what we did is:
Starting with the right-most column, 3 + 9 = 12
12 can't 'fit' in the "ones" column, so we put the "2" there and "carry" the leftover "10" to the 10's column
then we add that leftover 10 with the 40 and 20, which gives us 70
Of course, this is all familiar to us, but what I want to show you is that it is exactly the same with binary.
So, in this example, 5 + 7 = 12. But actually, what we did is:
1 + 1 = 2, but there is no such thing as "2" in binary. "2" is 10, so you put the "0" in place and you carry the "1"
which means you now have in the next column, 1 + 0 + 1 = 2, ditto, place a 0, carry the "1"
which means you have 1 + 1 + 1 = 3, "2" in binary is "11" so you put a "1" in place and you carry the other "1"
which leads you to the final sum of 1 + 0 + 0 = 1
As you can see in my example, I converted both numbers (0101 and 0111) to denary, and then I converted my answer (1100) into denary as well. This is useful to check that my maths is correct.
If you had a carry in the last sum, just like with denary, you merely go to the left one more place. In this example, we can see that we needed to go to the "hundreds" place, even though both of our initial numbers that we are adding only went to the "tens" place.
However, in computers, if you haven't programmed for this, it can be tricky!
In computers, when you have to go to "another place", it is called an overflow error. For example, if you were adding two four bit binary numbers together, and your answer is a five bit binary number. This results in an error, if you did not programme your computer to deal with having five bits.
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