# How do you calculate unit roundoff in a binary floating point system?

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## 2 Replies - 707 Views - Last Post: 07 December 2018 - 09:11 AM

### #1 B-ing

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# How do you calculate unit roundoff in a binary floating point system?

Posted 07 December 2018 - 08:53 AM

We define unit roundoff (u) as: The smallest positive number where the computed value of 1 + u is different from 1.

Let's consider an 8-bit binary floating point format with:

- a sign bit
- a 3-bit exponent
- a 4-bit mantissa with a hidden bit x0 = 1

How could I calculate the value of unit roundoff for this representation?
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## Replies To: How do you calculate unit roundoff in a binary floating point system?

### #2 modi123_1

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## Re: How do you calculate unit roundoff in a binary floating point system?

Posted 07 December 2018 - 08:57 AM

What have you tried, thought about, or considered?

### #3 B-ing

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## Re: How do you calculate unit roundoff in a binary floating point system?

Posted 07 December 2018 - 09:11 AM

This is how far I got:

1.000 + 0.0001 = 1.0001 which should get rounded to 1.001

This would mean that 0.0001 is the unit roundoff in this case, in binary though. This would then be 0.0625 in a decimal representation. I don't really understand where the hidden bit comes into play with all this.