Floating point computer - Trouble with getting back correct results

Having trouble with a challenge.

Let's say I have a th开发者_运维问答eoretical, base 10, floating point calculator with the following characteristics

• Only 3 digits for mantissa
• 1 digit for exponent
• Sign for mantissa and exponent

How would this machine compute the following?

300 + \sum_{i=1}^{100} 0.2

The correct result is 320. The machine's result is 300. But why? Can't get where the 20 goes goes missing...

Thanks for your time.

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Notwithstanding davin's answer, the number 0.2 is not 0: 2e-1 is representable in your system. What's happening here is that 300.2 is not representable to full precision, so 300 + 0.2 gets rounded down to 300. If you do this 100 times, you still end up with 300 :-)

Your system should be able to compute 300 + 100*0.2 correctly, however.

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The number 0.2 in this calculator is 0, because it should evaluate to 2 x 10^(-1), although the exponent has only 1 digit, which allows a range of 0 and 1, so -1 is outside its range. The underflow results in a truncation, which produces 0.

So if we sum 0 one hundred times and add the result to 300, we get 300.