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Let's say there is a floating-point code that fit in 16 bits, with 1 bit for the sign and 4 bits for the exponent and the rest (11) for the significad. I've been able to find the range of normalized exponent, which I believe is [-6,7], by calculating 1-bias and 2^(k-1) - 1. However, I'm having trouble finding these:

The median value of the code, the range of positive denormalized values, the range of positive normalized values, the median of the positive normalized values and the median of the positive values.

How can I calculate these? I'm not sure how to approach it.

Andrew
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    But usually, 1111 and 0000 at least are reserved for NaN/infinity and exact zero. – Lutz Lehmann Oct 18 '16 at 09:40
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    There are 16 bits. Only $2^{16} \approx 65000$ combinations. You can calculate each value into single or double precision on a PC (both should easily hold half precision float), stuff it in a list and then sort the list. – mathreadler Oct 18 '16 at 09:52
  • IEEE 754 has more negative than positive exponents, so range $[-7,6]$. – Lutz Lehmann Oct 18 '16 at 11:36

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