In computing, decimal64 is a decimal floatingpoint computer numbering format that occupies 8 bytes (64 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations.
Decimal64 supports 16 decimal digits of significand and an exponent range of −383 to +384, i.e. ±0.000000000000000×10^{−383} to ±9.999999999999999×10^{384}. (Equivalently, ±0000000000000000×10^{−398} to ±9999999999999999×10^{369}.) In contrast, the corresponding binary format, which is the most commonly used type, has an approximate range of ±0.000000000000001×10^{−308} to ±1.797693134862315×10^{308}. Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; 1×10^{2}=0.1×10^{3}=0.01×10^{4}, etc. Zero has 768 possible representations (1536 if you include both signed zeros).
Decimal64 floating point is a relatively new decimal floatingpoint format, formally introduced in the 2008 version^{[1]} of IEEE 754 as well as with ISO/IEC/IEEE 60559:2011.^{[2]}
Sign  Combination  Exponent continuation  Coefficient continuation 

1 bit  5 bits  8 bits  50 bits 
s  mmmmm  xxxxxxxx  cccccccccccccccccccccccccccccccccccccccccccccccccc 
IEEE 754 allows two alternative representation methods for decimal64 values. The standard does not specify how to signify which representation is used, for instance in a situation where decimal64 values are communicated between systems:
Both alternatives provide exactly the same range of representable numbers: 16 digits of significand and 3×2^{8} = 768 possible decimal exponent values. (All the possible decimal exponent values storable in a binary64 number are representable in decimal64, and most bits of the significand of a binary64 are stored keeping roughly the same number of decimal digits in the significand.)
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 5bit field. The remaining combinations encode infinities and NaNs.
Combination field  Exponent Msbits  Significand Msbits  Other 

00mmm  00  0xxx  — 
01mmm  01  0xxx  — 
10mmm  10  0xxx  — 
1100m  00  100x  — 
1101m  01  100x  — 
1110m  10  100x  — 
11110  —  —  ±Infinity 
11111  —  —  NaN. Sign bit ignored. First bit of exponent continuation field determines if NaN is signaling. 
In the cases of Infinity and NaN, all other bits of the encoding are ignored. Thus, it is possible to initialize an array to Infinities or NaNs by filling it with a single byte value.
This format uses a binary significand from 0 to 10^{16}−1 = 9999999999999999 = 2386F26FC0FFFF_{16} = 100011100001101111001001101111110000001111111111111111_{2}.
The encoding, completely stored on 64 bits, can represent binary significands up to 10×2^{50}−1 = 11258999068426239 = 27FFFFFFFFFFFF_{16}, but values larger than 10^{16}−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_{2} to 0111_{2}), or higher (1000_{2} or 1001_{2}).
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:
This includes subnormal numbers where the leading significand digit is 0.
If the 2 bits after the sign bit are "11", then the 10bit 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 3bit sequence "100" for the most bits of the true significand (in the remaining lower bits ttt...ttt of the significand, not all possible values are used).
The 2bit sequence "11" after the sign bit indicates that there is an implicit 3bit prefix "100" to the significand. Compare having an implicit 1bit prefix "1" in the significand of normal values for the binary formats. Note also that the 2bit sequences "00", "01", or "10" after the sign bit are part of the exponent field.
Note that the leading bits of the significand field do not encode the most significant decimal digit; they are simply part of a larger purebinary number. For example, a significand of 8000000000000000 is encoded as binary 011100011010111111010100100110001101000000000000000000_{2}, with the leading 4 bits encoding 7; the first significand which requires a 54th bit is 2^{53} = 9007199254740992. The highest valid significant is 9999999999999999 whose binary encoding is (100)011100001101111001001101111110000001111111111111111_{2} (with the 3 most significant bits (100) not stored but implicit as shown above; and the next bit is always zero in valid encodings).
In the above cases, the value represented is
If the four bits after the sign bit are "1111" then the value is an infinity or a NaN, as described above:
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 (DPD) encoding.
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 lesssignificant bits of the exponent.
The last 50 bits are the significand continuation field, consisting of five 10bit declets.^{[3]} Each declet encodes three decimal digits^{[3]} using the DPD encoding.
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):
If the first two bits after the sign bit are "11", then the second 2bits 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):
The remaining two combinations (11 110 and 11 111) of the 5bit field after the sign bit are used to represent ±infinity and NaNs, respectively.
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.
DPD encoded value  Decimal digits  

b9  b8  b7  b6  b5  b4  b3  b2  b1  b0  d2  d1  d0  Values encoded  Description  
a  b  c  d  e  f  0  g  h  i  0abc  0def  0ghi  (0–7) (0–7) (0–7)  Three small digits  
a  b  c  d  e  f  1  0  0  i  0abc  0def  100i  (0–7) (0–7) (8–9)  Two small digits, one large 

a  b  c  g  h  f  1  0  1  i  0abc  100f  0ghi  (0–7) (8–9) (0–7)  
g  h  c  d  e  f  1  1  0  i  100c  0def  0ghi  (8–9) (0–7) (0–7)  
g  h  c  0  0  f  1  1  1  i  100c  100f  0ghi  (8–9) (8–9) (0–7)  One small digit, two large 

d  e  c  0  1  f  1  1  1  i  100c  0def  100i  (8–9) (0–7) (8–9)  
a  b  c  1  0  f  1  1  1  i  0abc  100f  100i  (0–7) (8–9) (8–9)  
x  x  c  1  1  f  1  1  1  i  100c  100f  100i  (8–9) (8–9) (8–9)  Three large digits 
The 8 decimal values whose digits are all 8s or 9s have four codings each. The bits marked x in the table above are ignored on input, but will always be 0 in computed results. (The 8×3 = 24 nonstandard encodings fill in the gap between 10^{3}=1000 and 2^{10}=1024.)
In the above cases, with the true significand as the sequence of decimal digits decoded, the value represented is
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