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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 ...
It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. The number 2,147,483,647 remained the largest known prime until 1867. [4] In computing, this number is the largest value that a signed 32-bit integer field can hold.
The existing 64- and 128-bit formats follow this rule, but the 16- and 32-bit formats have more exponent bits (5 and 8 respectively) than this formula would provide (3 and 7 respectively). As with IEEE 754-1985, the biased-exponent field is filled with all 1 bits to indicate either infinity (trailing significand field = 0) or a NaN (trailing ...
On a typical computer system, a double-precision (64-bit) binary floating-point number has a coefficient of 53 bits (including 1 implied bit), an exponent of 11 bits, and 1 sign bit. Since 2 10 = 1024, the complete range of the positive normal floating-point numbers in this format is from 2 −1022 ≈ 2 × 10 −308 to approximately 2 1024 ≈ ...
The IEEE 754 floating-point standard defines the exponent field of a single-precision (32-bit) number as an 8-bit excess-127 field. The double-precision (64-bit) exponent field is an 11-bit excess-1023 field; see exponent bias. It also had use for binary-coded decimal numbers as excess-3.
The number of bits needed for the precision and range desired must be chosen to store the fractional and integer parts of a number. For instance, using a 32-bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit.
A 32-bit register can store 2 32 different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. With the two most common representations, the range is 0 through 4,294,967,295 (2 32 − 1) for representation as an binary number, and −2,147,483,648 (−2 31) through 2,147,483,647 (2 31 − 1) for representation as two's complement.
Floating-point formats. In computing, octuple precision is a binary floating-point -based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256- bit octuple precision is for applications requiring results in higher than quadruple precision.