Questions tagged [floating-point]

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

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2answers
752 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?
2
votes
3answers
538 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 ...
5
votes
1answer
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 ...
6
votes
2answers
307 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 ...
0
votes
2answers
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 ...
3
votes
1answer
17k views

Normalizing the mantissa in floating point representation

How to represent $0.148 * 2^{14}$ in normalized floating point arithmetic with the format 1 - Sign bit 7 - Exponent in Excess-64 form 8 - Mantissa $(0.148)_{10} =...
0
votes
1answer
594 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 ...
2
votes
1answer
1k views

Calculating Binet's formula for Fibonacci numbers with arbitrary precision

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 ...
18
votes
7answers
7k views

Why floating point representation uses a sign bit instead of 2's complement to indicate negative numbers

Consider a fixed point representation which can be regarded as a degenerate case of a floating number. It is entirely possible to use 2's complement for negative numbers. But why is a sign bit ...
14
votes
1answer
399 views

Floating point rounding

Can an IEEE-754 floating point number < 1 (i.e. generated with a random number generator which generates a number >= 0.0 and < 1.0) ever be multiplied by some integer (in floating point form) to ...