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Computing Academy GCSE Computer Science

• We wanted to

• We wanted to subtract 9 from 49. • We’ve converted the 9 into two’s complement • Now in order to perform the subtraction we actually add together the numbers. 256 128 64 32 16 8 4 2 1 0 0 1 1 0 0 0 1 + 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 This addition results in an overflow (e.g. the result has an extra bit on the left hand side – we started with 128, 64, 32, 16, 8, 4, 2, 1 – but we’d now need to have 256, 128, 64, 32, 16, 8, 4, 2, 1 in order to fit the result of this addition.) We don’t add an extra bit, we ignore and discard the overflow. So... 256 128 64 32 16 8 4 2 1 1 0 0 1 0 1 0 0 0 …becomes.. 128 64 32 16 8 4 2 1 0 0 1 0 1 0 0 0 69

If we convert the result back to decimal form.... 128 64 32 16 8 4 2 1 0 0 1 0 1 0 0 0 …we have 1 lot of 32 and one lot of 8 which is 40. Our original problem was 49 - 9 which is 40. So it worked! 70

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