More Simultaneous Dynamic Range with Fixed Point or Floating Point? What data path would have more simultaneous dynamic range: 32 bit fixed-point or 32 bit floating-point?  Why?
To clarify &quot;simultaneous dynamic range&quot;: This is the ability to discern strong and weak signals at the same time, while dynamic range is the total range between between the weakest signal (sensitivity to still meet a performance metric) and strongest signal (saturation or some other decrease in a performance metric such as 1 dB compression, clipping, etc). One example where we would be concerned with simultaneous dynamic range is in an FFT where we have both weak and strong tones simultaneously at two different frequencies and we want to be able to discern both in the same FFT result.
Our vision and hearing are good examples of the difference between simultaneous dynamic range and dynamic range: see https://en.wikipedia.org/wiki/Dynamic_range
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For the same total bit width, a fixed-point representation has a higher instantaneous dynamic range than a floating-point representation.
 For a value to be simultaneously including information about a strong and a weak signal (where the information is being carried by the sum of the strong and weak signal components), the weak signal has to have a value at least as large as the stronger signal's numerical error floor, given by the format's epsilon. In a floating-point representation, every bit allocated to the exponent similarly reduces the number of bits allocated to the significand, and thus increases the format's epsilon. This correspondingly decreases the ratio between the strong and weak signal components that can be included in a single value.
 For example in a standard 32-bit IEEE-754 single-precision floating point representation, 23 bits are allocated to the significand. As a result the smallest number that can be added to a given number $x$ is of the order of $x/2^{23}$ or approximately $8.6\times 10^6$ times smaller. Note that this is consistent with the C programming language's FLT_EPSILON which is approximately $1.19\times 10^{-7}$. In comparison, using a 32-bit fixed-point representation the smallest number that can be added to a large number using near full scale (e.g. 0xffffff00) is of the order of a single unit (e.g. 0x00000001) which is approximately $2^{32} \approx 4.3\times10^9$ times smaller.