# Questions tagged [floating-point]

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

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### Interpretation of '1/3' in IEEE floating point representation

For a rational number 1/3 below is the floating point representation(64 bit) of decimal expansion 0.3333333.... As per the above bit structure, I would like to ...
821 views

### What is 0.1 converted to 8bit IEEE754?

0.1 via $32\text{ bit}$ is rather easy: Sign: $0_2 = 0_{10}$ Exponent: $123_{10} = 01111011_2$ Mantissa: $5033165_{10} = 100110011001100110011001101_2$ Now, how do you calculate this, if you've ...
353 views

### Problem on Floating Point Representation

Consider the floating-point representation 31-24 : Exponent 23-0 : Mantissa The exponent is in 2's complement representation and mantissa is in the sign ...
55 views

### Rounding errors when converting floats to integers

Is it possible to have a rounding error when you convert a floating point number which can only be in increments of 0.01 to an integer by multiplying by 100 first? I would think that the lack of ...
198 views

### What's the algorithm for floating points equality test?

I've found that 0.1 + 0.2 == 0.3 is not true in Java (see this demo). So, I'm interested in how equality testing can be implemented for floats. Is there a ...
191 views

Hi I have this simple question. When adding a positive number with a negative number, both of same exponent. Imagine that after complementing the negative we have something like this: 1.111 + 0.001 .....
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### Product with floating point [closed]

I was studying the product with floating point and I saw this example. I made the translation, sorry if something is not grammatically correct. ![enter image description here]
723 views

### Machine epsilon vs least positive number

What is the difference between machine epsilon and least positive number in floating point representation? If I try to show the floating point number on a number line .Is the gap between exact 0 and ...
66 views

### Why is the precision of floating point numbers worse for smaller numbers?

Why is the machine error/epsilon higher between a pair of two lower numbers than a pair of two high numbers? For example, between the two smallest numbers possible in 5 bit mantissa and the two ...
217 views

### Gap between numbers in fixed-point vs. floating point arithmetic

If $r$ is a machine-representable number and $f(r)$ is the next larger machine representable number, are the following true or false? In fixed-point arithmetic, the distance between $r$ and $f(r)$ is ...
3k views

### Represent a real number without loss of precision

Current floating point (ANSI C float, double) allow to represent an approximation of a real number. Is there any way to represent real numbers without errors? Here's an idea I had, which is anything ...
80 views

### Floating point operations; Exception, Flags, and Trap Handlers

I am reading over the article found here specifically §D.4.4 Exceptions, Flags and Trap Handlers and am confused by the table D-4 in that section. Specifically the arguments sent to the trap handler ...
45 views

### floating point normalised value of -1

I have, lets say, 8 bits mantissa and 4 bit exponent. Then, -1=1111 1111 there are no 0s so how can I normalise -1 in 2's complement form?
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### 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....
324 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: $(-1)^{-s} * 1.M * 2^{E-bias}$ ...
123 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 ...
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 ...
310 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 ...
382 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 ...
606 views

### In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes

In a 32-bit floating number with normalized mantissa and excess-64 exponent base 16, the number $16^{-65}$ denotes Floating point overflow. Negative floating point overflow. All 0's in the exponent ...
Binet's formula for the nth Fibonacci numbers is remarkable because the equation "converts" via a few arithmetic operations an irrational number $\phi$ into an integer sequence. However, using finite ...