# Questions tagged [number-formats]

For questions about method for storing and manipulating numbers on computer systems, such as floating point or binary representations.

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### “Compressing” rationals given error bounds

I'm working on implementing some exact real arithmetic operations for fun. I've got the rough outline of how I want to do things as well and have figured out how to write most of the important ...
294 views

### Why is there more frequent overflow in normalised Floating Point

I read that overflow is more frequent when we work with normalised mantissas. Why is this? Is it because when we adopt a normalised representation, our range is smaller than in a unnormalised ...
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### Efficient algorithm for conversion of hexadecimal fraction to decimal fraction

Let's say I have some very long hex fraction like this: 0.3F30A21306AEFCBADE3230A593EFAEB395A39E What are some algorithms with an acceptable complexity to ...
81 views

### Why is a negative number a pseudo-positive number in ones' complement?

I'm studying ones' complement representation and I read in a book that a negative number in ones' complement is a pseudo-positive of value $R^n - 1 - |x|$. However there is no demostration and I can'...
1k views

### How do calculators convert from decimal to fraction?

Sorry if this question is either obvious or ignorant. I am a high school student with only the computer science knowledge I have taught myself. Calculators have a function that can convert numbers ...
49 views

### Why have only 15 bits been apportioned for the exponent in the 128-bit quad-precision datatype?

I look forward to the day we can start using quad-precision numbers, but was disappointed to see that in the specification, only 15 bits out of a whopping 128 were assigned to the exponent as shown by ...
431 views

### Convert 24(decimal) to modified IEEE 754 floating point format?

Here's what I have as the tweaked format I'm to use: S EEE MMMM (excess 8 format) s = sign bit, E = exponent bits, M = mantissa/fraction bits Otherwise, it follows the IEEE 754 in principle. The ...
4k views

### What does normalizing with hidden bit really mean?

I have a question related to representing numbers in base 2 with floating point. For example, if I have such a number $$0.000011 \cdot 2^3$$ then is its normalized form this? $$1.1\cdot 2^{-2}$$ ...
51 views

2k views

### Confused by Floating Point Spacing

I'm currently taking a numerical analysis class in college and we're covering floating point systems. For the most part, I have a good grasp on it. However, something I can't seem to visualize, and ...
183 views

### Show that only a few multiples of .01 decimal are powers of 2

I am asking this to advance the argument that BigDecimal is better than float or double for representing exact amounts of currency. Can someone refer me to a proof that between any two integers ...