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As a beginner I would like to know if this form of floating point number model (and possibly notation) has a distinguished name. In the model, a floating point number is defined by: $$ a = \pm m \cdot 2^k $$ where $$ m = \sum\limits_{i=1}^{t}m_i2^{-i} $$ $t\in\mathbb{N}, m_i\in\{0,1\}, m_1 = 1, k\in\mathbb{Z}$

So far I've tried Floating point and IEEE Floating point and I've seen that they're quite similar systems. I've read this model in a book and I'm trying to determine if the author is using an arbitrary model similar to IEEE Floating point or if this notation has a name on it's own (even if the model is a subset of IEEE's). Also I've found it disturbing that it's not stated in my book whether $\mathbb{N}$ refers to $\mathbb{N_0}$ or $\mathbb{N_1}$, even if $\mathbb{N_0}$ doesn't make sense for me here. So I've tried to check if there's another book|paper on this particular model, but I couldn't refer to my model without a name.

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Floating-point is a class of number representations. The model in your question is a generic example of a floating-point representation. IEEE floating-point is a particular instance of a floating-point representation, which you would get if you bounded the range of $k$ and $t$ and specified how to encode $\pm$, $m$, and $k$ in binary. – Rahul Jan 12 '13 at 18:25

It looks like you're just writing in binary numbers with finite support.

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