floating point number wikipedia - EAS

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  1. From Wikipedia, the free encyclopedia Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
    en.wikipedia.org/wiki/Single-precision_floating-point_format
    en.wikipedia.org/wiki/Single-precision_floating-point_format
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    What is a floating point number?
    在 計算機科學 中, 浮點 (英語: floating point ,縮寫為FP)是一種對於 實數 的近似值數值表現法,由一个 有效數字 (即 尾数 )加上 冪數 來表示,通常是乘以某个 基数 的整数次 指數 得到。 以這種表示法表示的數值,稱為 浮点數 ( floating-point number )。
    zh.wikipedia.org/wiki/%e6%b5%ae%e7%82%b9%e6%95%b0
    What is the base of floating point format?
    A floating-point format is specified by: 1 a base (also called radix) b, which is either 2 (binary) or 10 (decimal) in IEEE 754; 2 a precision p; 3 an exponent range from emin to emax, with emin = 1 − emax for all IEEE 754 formats.
    en.wikipedia.org/wiki/IEEE_754
    What is a floating point unit in Computer Science?
    A floating-point unit ( FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root.
    en.wikipedia.org/wiki/Floating-point_unit
    What is floating-point representation?
    One way computers bypass this problem is floating-point representation, with "floating" referring to how the radix point can move higher or lower when multiplied by an exponent (power) . In mathematics and science, very large and very small numbers are often made simpler and multiplied to a power of ten to make them easier to understand.
    simple.wikipedia.org/wiki/Floating_point
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    https://en.wikipedia.org/wiki/Floating-point_arithmetic

    A floating-point number consists of two fixed-point components, whose range depends exclusively on the number of bits or digits in their representation. Whereas components linearly depend on their range, the floating-point range linearly depends on the significand range and exponentially on the range … See more

    In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 … See more

    IEEE 754: floating point in modern computers image
    Dealing with exceptional cases  image

    In addition to the widely used IEEE 754 standard formats, other floating-point formats are used, or have been used, in certain domain-specific areas.
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    For ease of presentation and understanding, decimal radix with 7 digit precision will be used in the examples, as in the IEEE 754 … See more

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    Floating-point numbers
    A number representation specifies some way of encoding a number, usually as a string of digits.
    There are several … See more

    The IEEE standardized the computer representation for binary floating-point numbers in IEEE 754 (a.k.a. IEC 60559) in 1985. This first standard is followed by almost all modern … See more

    By their nature, all numbers expressed in floating-point format are rational numbers with a terminating expansion in the relevant base (for … See more

    Floating-point computation in a computer can run into three kinds of problems:
    • An operation can be mathematically undefined, such as ∞/∞, or division by zero.
    • An operation can be legal in principle, but not supported by the specific format, for example, … See more

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  4. https://simple.wikipedia.org/wiki/Floating_point
    • In mathematics and science, very large and very small numbers are often made simpler and multiplied to a power of ten to make them easier to understand. For example, it can be much easier to read 1.2 trillion as 1.2 × 10 12 {\displaystyle 1.2\times 10^{12}} than 1,200,000,000,000. This can also be used with negative powers of ten to make small numb...
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    • https://en.wikipedia.org/wiki/Single-precision_floating-point_format

      Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
      A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 …

    • https://en.wikipedia.org/wiki/Decimal_floating_point
      • Decimal floating-point arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions and binary fractions. The advantage of decimal floating-point representation over decimal f...
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      • https://en.wikipedia.org/wiki/Floating-point_unit
        • A floating-point unit is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root. Some FPUs can also perform various transcendental functions such as exponential or trigonometric calculations, but the accuracy can be ver...
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        • Estimated Reading Time: 8 mins
        • https://en.wikipedia.org/wiki/Double-precision_floating-point_format

          Floating point is used to represent fractional values, or when a wider range is needed than is …

        • https://en.wikipedia.org/wiki/IEEE_754

          The IEEE Standard for Floating-Point Arithmetic is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers. The standard addressed many problems found in the …

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