Are there any conventional rules for offset binary arithmetic with fixed size bit-width registers?

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Let's say we have two fixed sized binary numbers (8-bit), e.g. 00000101 (5) and 00100000 (32)

The task is to add them in offset binary (excess of 128). Are there any specific rules concerning how to go about this?

Would I for instance first convert both the numbers into offset binary notation, then add them and afterwards subtract the offset (because I added it twice)? But if so, what about overflow, given that the imaginary registers are only 8 bit wide?

Or would I first subtract the excess and then add the second number? Are there any conventional rules when it comes to offset binary arithmetic?

I'm preparing for an exam in computer architecture and computer data arithmetic. This has been a task on an exercise sheet in a previous term. I'v already searched the net extensively for answers but can't seem to find a solid one.

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1 Answers

I do not know what the "conventional rules" are for this operation, but I can tell you how I did this operation back when I did machine code.

This method works well when the offset is half the first number that overflows the register. That is the case for you, since the offset is 128 and the 8-bit register overflows on 256. This works especially well when the two numbers you want to add are already in the offset format.

The method is: add the two offset numbers, as unsigned addition and ignoring any overflow, then flip the most significant bit.

In your case, you are adding 10000101 (5 in offset) and 10100000 (32 in offset). Adding those results in 00100101, since there is overflow out of the most significant bit. Flipping the most-significant bit results in 10100101, which is indeed 37 in offset format.

This method may result in overflow, but only when the result is too positive or too negative to fit into the offset format anyway. And in most CPUs the two operations (unsigned addition and flipping the MSB) are practically trivial.

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