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In both cases, the most significant 4 bits of the significand (which actually only have 10 possible values) are combined with the most significant 2 bits of the exponent (3 possible values) to use 30 of the 32 possible values of a 5-bit field. The remaining combinations encode [[infinity|infinities]] and [[NaN]]s.
If the
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s
s
If the
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s
The following bits (''xxx...xxx'' in the above) encode the
The final combinations are used for infinities and NaNs, and are the same for both alternative encodings:
s
s
s
In the latter cases, all other ''xxx...xxx'' bits of the encoding are ignored. Thus, it is possible to initialize an array to NaNs by filling it with a single byte value.
=== Binary integer significand field ===
This format uses a binary significand from 0 to 10<sup>16</sup>−1 = {{gaps|9|999|999|999|999|999}} = 2386F26FC0FFFF<sub>16</sub> = {{gaps|1000|1110000110|1111001001|1011111100|0000111111|1111111111<sub>2</sub>}}.
The encoding, completely stored on 64 bits, can represent binary significands up to 10×2<sup>50</sup>−1 = {{gaps|11|258|999|068|426|239}} = 27FFFFFFFFFFFF<sub>16</sub>, but values larger than 10<sup>16</sup>−1 are illegal (and the standard requires implementations to treat them as 0, if encountered on input).
As described above, the encoding varies depending on whether the most significant 4 bits of the significand are in the range 0 to 7 (0000<sub>2</sub> to 0111<sub>2</sub>), or higher (1000<sub>2</sub> or 1001<sub>2</sub>).
If the 2 bits after the sign bit are "00", "01", or "10", then the exponent field consists of the 10 bits following the sign bit, and the significand is the remaining 53 bits, with an implicit leading 0 bit:
s 00 eeeeeeee [(0)ttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
s 01 eeeeeeee [(0)ttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
s 10 eeeeeeee [(0)ttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
This includes [[subnormal numbers]] where the leading significand digit is 0.
If the 4 bits after the sign bit are "1100", "1101", or "1110", then the 10-bit exponent field is shifted 2 bits to the right (after both the sign bit and the "11" bits thereafter), and the represented significand is in the remaining 51 bits. In this case there is an implicit (that is, not stored) leading 3-bit sequence "100"
s 11 00 eeeeeeee [(100)ttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
s 11 01 eeeeeeee [(100)ttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
s 11 10 eeeeeeee [(100)ttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt][tttttttt]
The
Note that the leading bits of the significand field do ''not'' encode the most significant decimal digit; they are simply part of a larger pure-binary number. For example, a significand of {{gaps|8|000|000|000|000|000}} is encoded as binary {{gaps|0111|0001101011|1111010100|1001100011|0100000000|0000000000}}, with the leading 4 bits encoding 7; the first significand which requires a 54th bit is 2<sup>53</sup> = {{gaps|9|007|199|254|740|992}}.
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=== Densely packed decimal significand field ===
In this version, the significand is stored as a series of decimal digits. The leading digit is between 0 and 9 (3 or 4 binary bits), and the rest of the significand uses the [[densely packed decimal]]
Unlike the binary integer significand version, where the exponent changed position and came before the significand, this encoding, combines the leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand into the five bits that follow the sign bit.
This eight bits after that are the exponent continuation field, providing the less-significant bits of the exponent.
The last 50 bits are the significand continuation field, consisting of 5 "declets" (10-bit
If the first two bits after the sign bit are "00", "01", or "10", then those are the leading bits of the exponent, and the three bits "TTT" after that are interpreted as the leading decimal digit (0 to 7):
s 00 TTT
s 01 TTT
s 10 TTT
If the 4 bits after the sign bit are "1100", "1101", or "1110", then the second 2-bits are the leading bits of the exponent, and the next bit "T" is prefixed with implicit bits "100" to form the leading decimal digit (8 or 9):
s
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s
The remaining two combinations (
The DPD/3BCD transcoding for the declets is given by the following table. b9...b0 are the bits of the DPD, and d2...d0 are the three BCD digits.
{{Densely packed decimal}}
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