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decimal32 supports 'normal' values, which can have 7 digit precision from ±1.000 000 × 10 ^ −95 up to ±9.999 999 × 10 ^ +96, plus 'subnormal' values with ramp-down relative precision down to ±1. × 10 ^ −101 (one digit), signed zeros, signed infinities and NaN (Not a Number). The encoding is somewhat complex, see below.
For example, the Decimal32 significand can be up to 10 7 −1 = 9 999 999 = 98967F 16 = 1001 1000100101 1001111111 2. While the encoding can represent larger significands, they are illegal and the standard requires implementations to treat them as 0, if encountered on input.
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Using the Decimal32 encoding (with a significand of 3*2+1 decimal digits) as an example (e stands for exponent, m for mantissa, i.e. significand): If the significand starts with 0mmm , omitting the leading 0 bit lets the significand fit into 23 bits:
Its integer part is the largest exponent shown on the output of a value in scientific notation with one leading digit in the significand before the decimal point (e.g. 1.698·10 38 is near the largest value in binary32, 9.999999·10 96 is the largest value in decimal32).
Floating-point formats; IEEE 754; 16-bit: Half (binary16) 32-bit: Single (binary32), decimal32 64-bit: Double (binary64), decimal64 128-bit: Quadruple (binary128 ...
For example, in the smallest decimal format in the table (decimal32), the range of positive normal numbers is 10 −95 through 9.999999 × 10 96. Non-zero numbers smaller in magnitude than the smallest normal number are called subnormal numbers (or denormal numbers). Zero is considered neither normal nor subnormal.
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