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Computing Academy GCSE Computer Science

Denary to Binary

Denary to Binary Performing conversation from denary to binary is also really simple. Let’s say we’d like to convert the denary number 37 into binary. First we’ll need our binary column headers. 128 64 32 16 8 4 2 1 Now, looking at our ‘target’ number of 37 we can ask ourselves, do we need 128 to get to 37? The answer is of course, no. 128 is too big. We can put a ‘0’ down in the 128 column. 128 64 32 16 8 4 2 1 0 We can then ask, do we need 64 to get to 37? The answer is again no as 64 is bigger than 36. We put down another 0 in the 64 column. 128 64 32 16 8 4 2 1 0 0 Next, we have 32. Can we use 32 to get to 37? Yes! 32 is smaller than our target of 37 so we can use it. We’ll put a ‘1’ in the 32 column to show that we’re using it. 128 64 32 16 8 4 2 1 0 0 1 We wanted 37, so far we have 32, so we’re still in need of 5. Can we use 16 to get 5? No: too big. Can we use 8 to get 5? No: too big. We can put ‘0’ down in the 16 and the 8 column. 59

128 64 32 16 8 4 2 1 0 0 1 0 0 Can we use 4 to get 5? Yes! So we can put down a ‘1’ in the 4 column. Now all we ned is a 1, so we put down a ‘0’ in the 2 column and a ‘1’ in the 1 column. 128 64 32 16 8 4 2 1 0 0 1 0 0 1 0 1 Lets check our answer by adding together those values represented by a 1: 32 + 4 + 1 = 37 So we are correct! The denary number 37 is represented as 00100101 in binary. 60

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