The IEEE 754-2008 standard includes decimal floating-point number formats in which the significand and the exponent (and the payloads of NaNs) can be encoded in two ways, referred to as binary encoding and decimal encoding.[1]
Both formats break a number down into a sign bit s, an exponent q (between qmin and qmax), and a p-digit significand c (between 0 and 10p−1). The value encoded is (−1)s×10q×c. In both formats the range of possible values is identical, but they differ in how the significand c is represented. In the decimal encoding, it is encoded as a series of p decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal (BID) encoding, it is encoded as a binary number.
^"DRAFT Standard for Floating Point Arithmetic P754" (PDF). 2006-10-04. Retrieved 2007-07-01.[permanent dead link]
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but requires a specialized decimal ALU to process. In the binaryintegerdecimal (BID) encoding, it is encoded as a binary number. Using the fact that...
lines, uses binary addressing, binaryinteger arithmetic, and binary floating point; it also includes instructions for packed decimalinteger arithmetic...
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different...
then throw away the integer part. For example, ( 1 3 ) 10 {\textstyle ({\frac {1}{3}})_{10}} , in binary, is: Thus the repeating decimal fraction 0.3... 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...
range [0,15]. A BCD to decimal decoder has ten output bits. It accepts an input value consisting of a binary-coded decimalinteger value and activates one...
"97" in decimal). Binary-coded decimal (BCD) is a binary encoded representation of integer values that uses a 4-bit nibble to encode decimal digits. Four...
groups of three (starting from the right, for integers). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the...
equivalent to 100 (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents...
right (least significant) side, advancing left. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first (i.e., the rightmost)...
Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base-16, "hexadecimal" (hex), number format. In the decimal system...
Densely packed decimal (DPD) is an efficient method for binary encoding decimal digits. The traditional system of binary encoding for decimal digits, known...
information) and binary (base-2) fractions. The advantage of decimal floating-point representation over decimal fixed-point and integer representation is...
rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called...
like a power of 10 in the decimal system. Two to the exponent of n, written as 2n, is the number of ways the bits in a binary word of length n can be arranged...
A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes...
with. Therefore, the decimal repeats: 0.0675675675.... For any integer fraction A/B, the remainder at step k, for any positive integer k, is A × 10k (modulo...
10 in absolute value, and nearly always written as a terminating decimal). The integer n is called the exponent and the real number m is called the significand...
{\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt {y}}} run...
adding them together (a binary addition, of course): 1011 (this is binary for decimal 11) × 1110 (this is binary for decimal 14) ====== 0000 (this is...
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