# Questions tagged [floating-point]

Approximate representation of numbers as a fixed number of digits multiplied by a logarithmic scale.

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### Why does floating point modulus exactness matters?

Most Smalltalk dialects currently implement a naive inexact floating modulus (fmod/remainder). I just changed this to improve Squeak/Pharo and eventually other Smalltalk adherence to standards (IEEE ...
225 views

### Can we improve the precision of IEEE floats by dropping leading zeros in the mantissa?

It seems like it would be possible to add more precision to the IEEE 32-bit mantissa system if the leading zeroes were also dropped, just like the leading 1 is dropped due to it being implicitly known....
100 views

### Floating point format: why must 1−emax ≤ q+p−1 ≤ emax?

From the Wikipedia page on the IEEE Standard for Floating-Point Arithmetic, The possible finite values that can be represented in a format are determined by the base (b), the number of digits in ...
322 views

### Problem in finding the floating point representation?

So, i was trying: $(-10.75)_{10}$ and to convert it into 32 bit binary floating point representation. i did this: According to IEEE standard: $(-1)^{-s} * 1.M * 2^{E-bias}$ ...
122 views

### When does the IEEE-754 64-bit float break as a counter

As a matter of curiosity I've been trying to determine at what point a 64-bit float no longer reflects the addition of 1 as expected; that is, at what point the digits as printed do not correspond to ...
801 views

### Implicit Leading 1 in Binary Floating Point

Is the convention of dropping the leading 1 when storing the significand a given in all binary floating point representations or not necessarily?
567 views

### Can a unnormalized floating point number be recognized also when exponent is not zero?

From Tanebaum's Structed Computer Organization. Exercise 4 of Appendix B The following binary floating-point number consist of a sign bit, an excess $64$, radix $2$ exponent, and a $16$-bit ...
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 ...
308 views

### What is the reason of inaccuracy of operations on float numbers?

I wonder why in JavaScript 0.1 + 0.2 // return 0.30000000000000004 4%0.1 // return 0.09999999999999978 http://jsbin.com/oHISAfU/1/edit (Example) In C the ...
381 views

### Implications of truncation of numbers when converted into binary

I have been posed with a question whereby a computer truncates numbers to x number of digits. Due to this, if this computer is trying to store a decimal number which has a binary equivalent greater ...
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