Here we have some data in a 5 by 5 grid of cards.
I'm going to make it more difficult for myself by adding another row and column to it.
The information represented in this grid is 'binary data' because it uses two values (black and white) to represent information.
The cards here have two sides, so we can represent a binary value by choosing which way up to put the card.
This data might be some text, or it might represent students' grades, or anything stored on a computer.
In reality this grid is just some random values, but let's imagine that it is some important data that we're relying on.
Change the cards to the following, starting in the top right and going clockwise: ⬛ Black, ⬛ Black, ⬜ White, ⬛ Black, ⬛ Black, ⬜ White, ⬜ White, ⬛ Black, ⬜ White, ⬜ White, ⬛ Black.
Then click 'Flip a bit'.
Now we are simulating transmitting the information and one bit gets changed.
The interactive has changed a card from black to white or white to black.
I'm going to see if I can work out which bit was changed.
Determine which bit has been changed by finding the bit at the intersection of the row and column which have an odd number of black squares.
I've found it!
It's this one.
Click on the appropriate bit and move the cursor to point to the green writing that should appear to the left of the interactive to confirm you were correct.
So what happened?
How did I do that so quickly?
Click the 'Start Over' button.
Firstly, when I said I was going to make it harder, I was actually making it easier by putting the data into parity.
Write in the chat what parity means to you.
Wait for some responses, if there aren't any responses prompt by asking what the mathematical term for pairs is (even amounts).
Let's take this step by step.
What state does F1 need to be in (white or black) to create even parity, an even number of black cards in row 1?
Type in the chat a "B" if you think black or "W" for white if you think white.
Wait for a couple of responses and respond accordingly.
Continue this for the remainder of column F, except the last bit in the bottom right corner.
Check that people aren't racing ahead for each co-ordinate by asking participants to keep pace with you.
Now let's look at the columns, starting with A6.
Type in the chat a "B" if you think black or "W" for white if you think white to make column A have an even number of black bits.
Continue for columns B to E.
And what about F6?
This is where we check we have completed the grid correctly, as the F column is the column we added to make all the rows have even parity.
What colour card do we need to complete row 6?
And what colour card do we need to complete column F?
Wait for a few responses.
That's right, it's the same colour to finish both row 8 and column H.
If it does work out the same when you're doing this with a class, then you can be confident that the other cards were put in correctly.
If it doesn't, you'll need to check back and see if one of the cards you've added is wrong.
Let's get the computer to flip a bit.
Wait for the “Confusation” to happen - the interactive will flip one card from black to white or white to black.
Note: For this next section, that you can click a row or column label in the interactive to 'circle' the row or column when talking about it.
With your knowledge of parity, can you find the card that was flipped?
Write in the chat the grid reference for the flipped card.
Allow time for responses in chat.
Let's check the suggested bit.
Click on the letter of the column suggested.
This will put a red rectangle around the selected column of bits.
We can see that this column has an uneven number of black bits, so we know one of these bits has been changed.
Lets go check the row.
Click on the number of the row suggested to bring up another red rectangle.
We can see that this row also has an uneven number of black bits.
So we know the bit at the intersection of these two red rectangles is the bit that was changed.
Let's click on this bit and see if we were right.
Click on the card and see if you are correct.