1.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82 Converted to 64 Bit Double Precision IEEE 754 Binary Floating Point Representation Standard

Convert decimal 1.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82(10) to 64 bit double precision IEEE 754 binary floating point representation standard (1 bit for sign, 11 bits for exponent, 52 bits for mantissa)

What are the steps to convert decimal number
1.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82(10) to 64 bit double precision IEEE 754 binary floating point representation (1 bit for sign, 11 bits for exponent, 52 bits for mantissa)

1. First, convert to binary (in base 2) the integer part: 1.
Divide the number repeatedly by 2.

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the integer part of the number.

Take all the remainders starting from the bottom of the list constructed above.

1(10) =

1(2)


3. Convert to binary (base 2) the fractional part: 0.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82.

Multiply it repeatedly by 2.

Keep track of each integer part of the results.

Stop when we get a fractional part that is equal to zero.


  • #) multiplying = integer + fractional part;
  • 1) 0.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82 × 2 = 0 + 0.666 666 666 666 666 518 636 930 049 979 127 943 515 779 64;
  • 2) 0.666 666 666 666 666 518 636 930 049 979 127 943 515 779 64 × 2 = 1 + 0.333 333 333 333 333 037 273 860 099 958 255 887 031 559 28;
  • 3) 0.333 333 333 333 333 037 273 860 099 958 255 887 031 559 28 × 2 = 0 + 0.666 666 666 666 666 074 547 720 199 916 511 774 063 118 56;
  • 4) 0.666 666 666 666 666 074 547 720 199 916 511 774 063 118 56 × 2 = 1 + 0.333 333 333 333 332 149 095 440 399 833 023 548 126 237 12;
  • 5) 0.333 333 333 333 332 149 095 440 399 833 023 548 126 237 12 × 2 = 0 + 0.666 666 666 666 664 298 190 880 799 666 047 096 252 474 24;
  • 6) 0.666 666 666 666 664 298 190 880 799 666 047 096 252 474 24 × 2 = 1 + 0.333 333 333 333 328 596 381 761 599 332 094 192 504 948 48;
  • 7) 0.333 333 333 333 328 596 381 761 599 332 094 192 504 948 48 × 2 = 0 + 0.666 666 666 666 657 192 763 523 198 664 188 385 009 896 96;
  • 8) 0.666 666 666 666 657 192 763 523 198 664 188 385 009 896 96 × 2 = 1 + 0.333 333 333 333 314 385 527 046 397 328 376 770 019 793 92;
  • 9) 0.333 333 333 333 314 385 527 046 397 328 376 770 019 793 92 × 2 = 0 + 0.666 666 666 666 628 771 054 092 794 656 753 540 039 587 84;
  • 10) 0.666 666 666 666 628 771 054 092 794 656 753 540 039 587 84 × 2 = 1 + 0.333 333 333 333 257 542 108 185 589 313 507 080 079 175 68;
  • 11) 0.333 333 333 333 257 542 108 185 589 313 507 080 079 175 68 × 2 = 0 + 0.666 666 666 666 515 084 216 371 178 627 014 160 158 351 36;
  • 12) 0.666 666 666 666 515 084 216 371 178 627 014 160 158 351 36 × 2 = 1 + 0.333 333 333 333 030 168 432 742 357 254 028 320 316 702 72;
  • 13) 0.333 333 333 333 030 168 432 742 357 254 028 320 316 702 72 × 2 = 0 + 0.666 666 666 666 060 336 865 484 714 508 056 640 633 405 44;
  • 14) 0.666 666 666 666 060 336 865 484 714 508 056 640 633 405 44 × 2 = 1 + 0.333 333 333 332 120 673 730 969 429 016 113 281 266 810 88;
  • 15) 0.333 333 333 332 120 673 730 969 429 016 113 281 266 810 88 × 2 = 0 + 0.666 666 666 664 241 347 461 938 858 032 226 562 533 621 76;
  • 16) 0.666 666 666 664 241 347 461 938 858 032 226 562 533 621 76 × 2 = 1 + 0.333 333 333 328 482 694 923 877 716 064 453 125 067 243 52;
  • 17) 0.333 333 333 328 482 694 923 877 716 064 453 125 067 243 52 × 2 = 0 + 0.666 666 666 656 965 389 847 755 432 128 906 250 134 487 04;
  • 18) 0.666 666 666 656 965 389 847 755 432 128 906 250 134 487 04 × 2 = 1 + 0.333 333 333 313 930 779 695 510 864 257 812 500 268 974 08;
  • 19) 0.333 333 333 313 930 779 695 510 864 257 812 500 268 974 08 × 2 = 0 + 0.666 666 666 627 861 559 391 021 728 515 625 000 537 948 16;
  • 20) 0.666 666 666 627 861 559 391 021 728 515 625 000 537 948 16 × 2 = 1 + 0.333 333 333 255 723 118 782 043 457 031 250 001 075 896 32;
  • 21) 0.333 333 333 255 723 118 782 043 457 031 250 001 075 896 32 × 2 = 0 + 0.666 666 666 511 446 237 564 086 914 062 500 002 151 792 64;
  • 22) 0.666 666 666 511 446 237 564 086 914 062 500 002 151 792 64 × 2 = 1 + 0.333 333 333 022 892 475 128 173 828 125 000 004 303 585 28;
  • 23) 0.333 333 333 022 892 475 128 173 828 125 000 004 303 585 28 × 2 = 0 + 0.666 666 666 045 784 950 256 347 656 250 000 008 607 170 56;
  • 24) 0.666 666 666 045 784 950 256 347 656 250 000 008 607 170 56 × 2 = 1 + 0.333 333 332 091 569 900 512 695 312 500 000 017 214 341 12;
  • 25) 0.333 333 332 091 569 900 512 695 312 500 000 017 214 341 12 × 2 = 0 + 0.666 666 664 183 139 801 025 390 625 000 000 034 428 682 24;
  • 26) 0.666 666 664 183 139 801 025 390 625 000 000 034 428 682 24 × 2 = 1 + 0.333 333 328 366 279 602 050 781 250 000 000 068 857 364 48;
  • 27) 0.333 333 328 366 279 602 050 781 250 000 000 068 857 364 48 × 2 = 0 + 0.666 666 656 732 559 204 101 562 500 000 000 137 714 728 96;
  • 28) 0.666 666 656 732 559 204 101 562 500 000 000 137 714 728 96 × 2 = 1 + 0.333 333 313 465 118 408 203 125 000 000 000 275 429 457 92;
  • 29) 0.333 333 313 465 118 408 203 125 000 000 000 275 429 457 92 × 2 = 0 + 0.666 666 626 930 236 816 406 250 000 000 000 550 858 915 84;
  • 30) 0.666 666 626 930 236 816 406 250 000 000 000 550 858 915 84 × 2 = 1 + 0.333 333 253 860 473 632 812 500 000 000 001 101 717 831 68;
  • 31) 0.333 333 253 860 473 632 812 500 000 000 001 101 717 831 68 × 2 = 0 + 0.666 666 507 720 947 265 625 000 000 000 002 203 435 663 36;
  • 32) 0.666 666 507 720 947 265 625 000 000 000 002 203 435 663 36 × 2 = 1 + 0.333 333 015 441 894 531 250 000 000 000 004 406 871 326 72;
  • 33) 0.333 333 015 441 894 531 250 000 000 000 004 406 871 326 72 × 2 = 0 + 0.666 666 030 883 789 062 500 000 000 000 008 813 742 653 44;
  • 34) 0.666 666 030 883 789 062 500 000 000 000 008 813 742 653 44 × 2 = 1 + 0.333 332 061 767 578 125 000 000 000 000 017 627 485 306 88;
  • 35) 0.333 332 061 767 578 125 000 000 000 000 017 627 485 306 88 × 2 = 0 + 0.666 664 123 535 156 250 000 000 000 000 035 254 970 613 76;
  • 36) 0.666 664 123 535 156 250 000 000 000 000 035 254 970 613 76 × 2 = 1 + 0.333 328 247 070 312 500 000 000 000 000 070 509 941 227 52;
  • 37) 0.333 328 247 070 312 500 000 000 000 000 070 509 941 227 52 × 2 = 0 + 0.666 656 494 140 625 000 000 000 000 000 141 019 882 455 04;
  • 38) 0.666 656 494 140 625 000 000 000 000 000 141 019 882 455 04 × 2 = 1 + 0.333 312 988 281 250 000 000 000 000 000 282 039 764 910 08;
  • 39) 0.333 312 988 281 250 000 000 000 000 000 282 039 764 910 08 × 2 = 0 + 0.666 625 976 562 500 000 000 000 000 000 564 079 529 820 16;
  • 40) 0.666 625 976 562 500 000 000 000 000 000 564 079 529 820 16 × 2 = 1 + 0.333 251 953 125 000 000 000 000 000 001 128 159 059 640 32;
  • 41) 0.333 251 953 125 000 000 000 000 000 001 128 159 059 640 32 × 2 = 0 + 0.666 503 906 250 000 000 000 000 000 002 256 318 119 280 64;
  • 42) 0.666 503 906 250 000 000 000 000 000 002 256 318 119 280 64 × 2 = 1 + 0.333 007 812 500 000 000 000 000 000 004 512 636 238 561 28;
  • 43) 0.333 007 812 500 000 000 000 000 000 004 512 636 238 561 28 × 2 = 0 + 0.666 015 625 000 000 000 000 000 000 009 025 272 477 122 56;
  • 44) 0.666 015 625 000 000 000 000 000 000 009 025 272 477 122 56 × 2 = 1 + 0.332 031 250 000 000 000 000 000 000 018 050 544 954 245 12;
  • 45) 0.332 031 250 000 000 000 000 000 000 018 050 544 954 245 12 × 2 = 0 + 0.664 062 500 000 000 000 000 000 000 036 101 089 908 490 24;
  • 46) 0.664 062 500 000 000 000 000 000 000 036 101 089 908 490 24 × 2 = 1 + 0.328 125 000 000 000 000 000 000 000 072 202 179 816 980 48;
  • 47) 0.328 125 000 000 000 000 000 000 000 072 202 179 816 980 48 × 2 = 0 + 0.656 250 000 000 000 000 000 000 000 144 404 359 633 960 96;
  • 48) 0.656 250 000 000 000 000 000 000 000 144 404 359 633 960 96 × 2 = 1 + 0.312 500 000 000 000 000 000 000 000 288 808 719 267 921 92;
  • 49) 0.312 500 000 000 000 000 000 000 000 288 808 719 267 921 92 × 2 = 0 + 0.625 000 000 000 000 000 000 000 000 577 617 438 535 843 84;
  • 50) 0.625 000 000 000 000 000 000 000 000 577 617 438 535 843 84 × 2 = 1 + 0.250 000 000 000 000 000 000 000 001 155 234 877 071 687 68;
  • 51) 0.250 000 000 000 000 000 000 000 001 155 234 877 071 687 68 × 2 = 0 + 0.500 000 000 000 000 000 000 000 002 310 469 754 143 375 36;
  • 52) 0.500 000 000 000 000 000 000 000 002 310 469 754 143 375 36 × 2 = 1 + 0.000 000 000 000 000 000 000 000 004 620 939 508 286 750 72;
  • 53) 0.000 000 000 000 000 000 000 000 004 620 939 508 286 750 72 × 2 = 0 + 0.000 000 000 000 000 000 000 000 009 241 879 016 573 501 44;

We didn't get any fractional part that was equal to zero. But we had enough iterations (over Mantissa limit) and at least one integer that was different from zero => FULL STOP (Losing precision - the converted number we get in the end will be just a very good approximation of the initial one).


4. Construct the base 2 representation of the fractional part of the number.

Take all the integer parts of the multiplying operations, starting from the top of the constructed list above:


0.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82(10) =

0.0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0(2)

5. Positive number before normalization:

1.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82(10) =

1.0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0(2)

6. Normalize the binary representation of the number.

Shift the decimal mark 0 positions to the left, so that only one non zero digit remains to the left of it:


1.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82(10) =

1.0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0(2) =

1.0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0(2) × 20


7. Up to this moment, there are the following elements that would feed into the 64 bit double precision IEEE 754 binary floating point representation:

Sign 0 (a positive number)

Exponent (unadjusted): 0

Mantissa (not normalized):
1.0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0


8. Adjust the exponent.

Use the 11 bit excess/bias notation:


Exponent (adjusted) =

Exponent (unadjusted) + 2(11-1) - 1 =

0 + 2(11-1) - 1 =

(0 + 1 023)(10) =

1 023(10)


9. Convert the adjusted exponent from the decimal (base 10) to 11 bit binary.

Use the same technique of repeatedly dividing by 2:


  • division = quotient + remainder;
  • 1 023 ÷ 2 = 511 + 1;
  • 511 ÷ 2 = 255 + 1;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 1 ÷ 2 = 0 + 1;

10. Construct the base 2 representation of the adjusted exponent.

Take all the remainders starting from the bottom of the list constructed above.


Exponent (adjusted) =

1023(10) =

011 1111 1111(2)


11. Normalize the mantissa.

a) Remove the leading (the leftmost) bit, since it's allways 1, and the decimal point, if the case.

b) Adjust its length to 52 bits, by removing the excess bits, from the right (if any of the excess bits is set on 1, we are losing precision...).


Mantissa (normalized) =

1. 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0 =

0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101


12. The three elements that make up the number's 64 bit double precision IEEE 754 binary floating point representation:

Sign (1 bit) =
0 (a positive number)

Exponent (11 bits) =
011 1111 1111

Mantissa (52 bits) =
0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101


Decimal number 1.333 333 333 333 333 259 318 465 024 989 563 971 757 889 82 converted to 64 bit double precision IEEE 754 binary floating point representation:

0 - 011 1111 1111 - 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101 0101

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How to convert numbers from the decimal system (base ten) to 64 bit double precision IEEE 754 binary floating point standard

Follow the steps below to convert a base 10 decimal number to 64 bit double precision IEEE 754 binary floating point:

  • 1. If the number to be converted is negative, start with its the positive version.
  • 2. First convert the integer part. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, until we get a quotient that is equal to zero, keeping track of each remainder.
  • 3. Construct the base 2 representation of the positive integer part of the number, by taking all the remainders from the previous operations, starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Then convert the fractional part. Multiply the number repeatedly by 2, until we get a fractional part that is equal to zero, keeping track of each integer part of the results.
  • 5. Construct the base 2 representation of the fractional part of the number, by taking all the integer parts of the multiplying operations, starting from the top of the list constructed above (they should appear in the binary representation, from left to right, in the order they have been calculated).
  • 6. Normalize the binary representation of the number, shifting the decimal mark (the decimal point) "n" positions either to the left, or to the right, so that only one non zero digit remains to the left of the decimal mark.
  • 7. Adjust the exponent in 11 bit excess/bias notation and then convert it from decimal (base 10) to 11 bit binary, by using the same technique of repeatedly dividing by 2, as shown above:
    Exponent (adjusted) = Exponent (unadjusted) + 2(11-1) - 1
  • 8. Normalize mantissa, remove the leading (leftmost) bit, since it's allways '1' (and the decimal mark, if the case) and adjust its length to 52 bits, either by removing the excess bits from the right (losing precision...) or by adding extra bits set on '0' to the right.
  • 9. Sign (it takes 1 bit) is either 1 for a negative or 0 for a positive number.

Example: convert the negative number -31.640 215 from the decimal system (base ten) to 64 bit double precision IEEE 754 binary floating point:

  • 1. Start with the positive version of the number:

    |-31.640 215| = 31.640 215

  • 2. First convert the integer part, 31. Divide it repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder;
    • 31 ÷ 2 = 15 + 1;
    • 15 ÷ 2 = 7 + 1;
    • 7 ÷ 2 = 3 + 1;
    • 3 ÷ 2 = 1 + 1;
    • 1 ÷ 2 = 0 + 1;
    • We have encountered a quotient that is ZERO => FULL STOP
  • 3. Construct the base 2 representation of the integer part of the number by taking all the remainders of the previous dividing operations, starting from the bottom of the list constructed above:

    31(10) = 1 1111(2)

  • 4. Then, convert the fractional part, 0.640 215. Multiply repeatedly by 2, keeping track of each integer part of the results, until we get a fractional part that is equal to zero:
    • #) multiplying = integer + fractional part;
    • 1) 0.640 215 × 2 = 1 + 0.280 43;
    • 2) 0.280 43 × 2 = 0 + 0.560 86;
    • 3) 0.560 86 × 2 = 1 + 0.121 72;
    • 4) 0.121 72 × 2 = 0 + 0.243 44;
    • 5) 0.243 44 × 2 = 0 + 0.486 88;
    • 6) 0.486 88 × 2 = 0 + 0.973 76;
    • 7) 0.973 76 × 2 = 1 + 0.947 52;
    • 8) 0.947 52 × 2 = 1 + 0.895 04;
    • 9) 0.895 04 × 2 = 1 + 0.790 08;
    • 10) 0.790 08 × 2 = 1 + 0.580 16;
    • 11) 0.580 16 × 2 = 1 + 0.160 32;
    • 12) 0.160 32 × 2 = 0 + 0.320 64;
    • 13) 0.320 64 × 2 = 0 + 0.641 28;
    • 14) 0.641 28 × 2 = 1 + 0.282 56;
    • 15) 0.282 56 × 2 = 0 + 0.565 12;
    • 16) 0.565 12 × 2 = 1 + 0.130 24;
    • 17) 0.130 24 × 2 = 0 + 0.260 48;
    • 18) 0.260 48 × 2 = 0 + 0.520 96;
    • 19) 0.520 96 × 2 = 1 + 0.041 92;
    • 20) 0.041 92 × 2 = 0 + 0.083 84;
    • 21) 0.083 84 × 2 = 0 + 0.167 68;
    • 22) 0.167 68 × 2 = 0 + 0.335 36;
    • 23) 0.335 36 × 2 = 0 + 0.670 72;
    • 24) 0.670 72 × 2 = 1 + 0.341 44;
    • 25) 0.341 44 × 2 = 0 + 0.682 88;
    • 26) 0.682 88 × 2 = 1 + 0.365 76;
    • 27) 0.365 76 × 2 = 0 + 0.731 52;
    • 28) 0.731 52 × 2 = 1 + 0.463 04;
    • 29) 0.463 04 × 2 = 0 + 0.926 08;
    • 30) 0.926 08 × 2 = 1 + 0.852 16;
    • 31) 0.852 16 × 2 = 1 + 0.704 32;
    • 32) 0.704 32 × 2 = 1 + 0.408 64;
    • 33) 0.408 64 × 2 = 0 + 0.817 28;
    • 34) 0.817 28 × 2 = 1 + 0.634 56;
    • 35) 0.634 56 × 2 = 1 + 0.269 12;
    • 36) 0.269 12 × 2 = 0 + 0.538 24;
    • 37) 0.538 24 × 2 = 1 + 0.076 48;
    • 38) 0.076 48 × 2 = 0 + 0.152 96;
    • 39) 0.152 96 × 2 = 0 + 0.305 92;
    • 40) 0.305 92 × 2 = 0 + 0.611 84;
    • 41) 0.611 84 × 2 = 1 + 0.223 68;
    • 42) 0.223 68 × 2 = 0 + 0.447 36;
    • 43) 0.447 36 × 2 = 0 + 0.894 72;
    • 44) 0.894 72 × 2 = 1 + 0.789 44;
    • 45) 0.789 44 × 2 = 1 + 0.578 88;
    • 46) 0.578 88 × 2 = 1 + 0.157 76;
    • 47) 0.157 76 × 2 = 0 + 0.315 52;
    • 48) 0.315 52 × 2 = 0 + 0.631 04;
    • 49) 0.631 04 × 2 = 1 + 0.262 08;
    • 50) 0.262 08 × 2 = 0 + 0.524 16;
    • 51) 0.524 16 × 2 = 1 + 0.048 32;
    • 52) 0.048 32 × 2 = 0 + 0.096 64;
    • 53) 0.096 64 × 2 = 0 + 0.193 28;
    • We didn't get any fractional part that was equal to zero. But we had enough iterations (over Mantissa limit = 52) and at least one integer part that was different from zero => FULL STOP (losing precision...).
  • 5. Construct the base 2 representation of the fractional part of the number, by taking all the integer parts of the previous multiplying operations, starting from the top of the constructed list above:

    0.640 215(10) = 0.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2)

  • 6. Summarizing - the positive number before normalization:

    31.640 215(10) = 1 1111.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2)

  • 7. Normalize the binary representation of the number, shifting the decimal mark 4 positions to the left so that only one non-zero digit stays to the left of the decimal mark:

    31.640 215(10) =
    1 1111.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2) =
    1 1111.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2) × 20 =
    1.1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2) × 24

  • 8. Up to this moment, there are the following elements that would feed into the 64 bit double precision IEEE 754 binary floating point representation:

    Sign: 1 (a negative number)

    Exponent (unadjusted): 4

    Mantissa (not-normalized): 1.1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0

  • 9. Adjust the exponent in 11 bit excess/bias notation and then convert it from decimal (base 10) to 11 bit binary (base 2), by using the same technique of repeatedly dividing it by 2, as shown above:

    Exponent (adjusted) = Exponent (unadjusted) + 2(11-1) - 1 = (4 + 1023)(10) = 1027(10) =
    100 0000 0011(2)

  • 10. Normalize mantissa, remove the leading (leftmost) bit, since it's allways '1' (and the decimal sign) and adjust its length to 52 bits, by removing the excess bits, from the right (losing precision...):

    Mantissa (not-normalized): 1.1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0

    Mantissa (normalized): 1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100

  • Conclusion:

    Sign (1 bit) = 1 (a negative number)

    Exponent (8 bits) = 100 0000 0011

    Mantissa (52 bits) = 1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100

  • Number -31.640 215, converted from decimal system (base 10) to 64 bit double precision IEEE 754 binary floating point =
    1 - 100 0000 0011 - 1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100