IEEE 754 is a standard for normalizing so that the computer can represent real numbers from base-2 (binary).
The binary system is used because it has a higher performance in dealing with calculations.
✅ - This repository is for the authors own teaching purposes and is definitely not a blog post.
✅ - There is no lack of references on the Internet for understanding the problem.
✅ - Such that the goal is to experience these events as representation errors, precision, rounding, comparison and propagation. So that it is possible to understand in practice and implement alternatives.
✅ - The language chosen for the practical exercise was Javascript. But, the phenomenon happens in most programming languages and development environments.
Given a range of values, we need to deal with the trade-off between representing as many values as possible and how to represent them accurately.
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The Double Precision system can store more values and with higher accuracy, since it has a higher capacity for significant digits (52 values) versus (23 vaulues) in single precision.
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5.25 in base-2
> +(5.25).toString(2)
output: 101.01-
Just as we cannot represent the fractional value (1/3) in the decimal base such that the value is (0.333333333...). In the binary system, it is no different. In some cases it is impossible to represent a number with 100% accuracy.
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There is no such thing as infinite precision, since computer memory is finite.
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One technique for representing fractional numbers in binary is to work with negative powers of an integer. In this way, it is possible to represent fractional quantities of an integer.
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The use of binary numbers increases the performance of the computer when doing calculations. If there is a need for coverage because of the sensitivity of exact values in a '$FOO' application, this challenge is in the hands of the developer.
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Since Javascript does not have a native decimal type like in Java (BigDecimal), a widely used alternative is to install libraries that can use a decimal of limited precision.
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