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Between an adjacent pair of nonzero IEEE single precision real numbers, how many IEEE double precision numbers are there?

I was also wondering if this question has something to do with the hidden bit.

Can anyone help me?

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  • $\begingroup$ How many mantissa bits in single and double precision? The difference should give you the solution. $\endgroup$ – gnasher729 Sep 26 '18 at 17:46
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Let's consider two made-up number systems: 2-dec and 3-dec. In 2-dec, numbers are specified to two decimal points (in decimal). In 3-dec, it's three. Between, say, 1.2 and 1.3, which are adjacent in 2-dec, we have 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29 in 3-dec.

Hope this helps.

As an aside, the answer might potentially depend on whether the numbers are denormalized or not.

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