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Conversely, precision can be lost when converting representations from integer to floating-point, since a floating-point type may be unable to exactly represent all possible values of some integer type. For example, float might be an IEEE 754 single precision type, which cannot represent the integer 16777217 exactly, while a 32-bit integer type ...
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. The fractional bits continue the pattern set by the integer bits. The next bit is the half's bit, then the quarter's bit, then the ⅛'s bit, and so on. For example:
Sign bit: 1 bit; Exponent: 11 bits; Significand precision: 53 bits (52 explicitly stored) The sign bit determines the sign of the number (including when this number is zero, which is signed). The exponent field is an 11-bit unsigned integer from 0 to 2047, in biased form: an exponent value of 1023 represents the actual zero. Exponents range ...
In the Alpha architecture, a byte is defined as an 8-bit datum (octet), a word as a 16-bit datum, a longword as a 32-bit datum, a quadword as a 64-bit datum, and an octaword as a 128-bit datum. The Alpha architecture originally defined six data types: Quadword (64-bit) integer; Longword (32-bit) integer; IEEE T-floating-point (double precision ...
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 ...
Usually, the 32-bit and 64-bit IEEE 754 binary floating-point formats are used for float and double respectively. The C99 standard includes new real floating-point types float_t and double_t, defined in <math.h>. They correspond to the types used for the intermediate results of floating-point expressions when FLT_EVAL_METHOD is 0, 1, or 2.
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In the decimal encoding, the 16-digit significand is represented as a decimal coded positive integer, based on densely packed decimal (DPD) with 5 groups of 3 digits (except the most significant digit encoded specially) are each represented in declets (10-bit sequences).