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Converting Binary Numbers

As part of the iGCSE, you will be required to convert binary number to and from denary, our base 10 number system.

We’ve already seen that binary uses powers of 2 to convert from Denary (base 10) to Binary (base 2), and using the conversion table below is a useful way to help you to convert as you will not have a calculator in your exam:

128  64  32  16  8  4  2  1
 0   0   1   0   1  0  1  0

In the table above, we’ve converted the number 42 into binary by placing the powers of 2 in different columns and placing a 1 under the numbers that you would use to add up to 42. So in this case: 32 + 8 + 2 = 42

We can use this process in reverse to convert a binary number back into denary by writing the powers of 2 over each digit and adding up the columns with a 1 in. If your binary number is longer than 8 digits (bits) just keep doubling the numbers in the columns!

Activity – Practice Questions

Once you have completed the video lesson at the top of the page, download this practice sheet and test your understanding of the conversions. Use the second page to check your answers.

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