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Several earlier 16-bit floating point formats have existed including that of Hitachi's HD61810 DSP of 1982 (a 4-bit exponent and a 12-bit mantissa), [2] Thomas J. Scott's WIF of 1991 (5 exponent bits, 10 mantissa bits) [3] and the 3dfx Voodoo Graphics processor of 1995 (same as Hitachi).
For numbers with a base-2 exponent part of 0, i.e. numbers with an absolute value higher than or equal to 1 but lower than 2, an ULP is exactly 2 −23 or about 10 −7 in single precision, and exactly 2 −53 or about 10 −16 in double precision. The mandated behavior of IEEE-compliant hardware is that the result be within one-half of a ULP.
The leading digit is between 0 and 9 (3 or 4 binary bits), and the rest of the significand uses the densely packed decimal (DPD) encoding. The leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand are combined into the five bits that follow the sign bit. This is followed by a fixed-offset exponent continuation field.
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Given the hexadecimal representation 3FD5 5555 5555 5555 16, Sign = 0 Exponent = 3FD 16 = 1021 Exponent Bias = 1023 (constant value; see above) Fraction = 5 5555 5555 5555 16 Value = 2 (Exponent − Exponent Bias) × 1.Fraction – Note that Fraction must not be converted to decimal here = 2 −2 × (15 5555 5555 5555 16 × 2 −52) = 2 −54 ...
The decimal numeral system (also called the base-ten positional numeral system and denary / ˈ d iː n ər i / [1] or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal ...
In computer architecture, 16-bit integers, memory addresses, or other data units are those that are 16 bits (2 octets) wide.Also, 16-bit central processing unit (CPU) and arithmetic logic unit (ALU) architectures are those that are based on registers, address buses, or data buses of that size. 16-bit microcomputers are microcomputers that use 16-bit microprocessors.
Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two , e.g. 1 / 8 = 1 / 2 3 .
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