Converter: 64 bit double precision IEEE 754 binary floating point numbers converted to decimal base ten (double)

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Exponent: empty
Mantissa: empty

Convert 64 bit double precision IEEE 754 floating point standard binary numbers to base ten decimal system (double)

64 bit double precision IEEE 754 binary floating point standard representation of numbers requires three building blocks: sign (it takes 1 bit and it's either 0 for positive or 1 for negative numbers), exponent (11 bits), mantissa (52 bits)

Latest 64 bit double precision IEEE 754 floating point binary standard numbers converted to decimal base ten (double)

0 - 100 0111 1110 - 1111 1111 1111 1111 1111 1101 0101 1000 0110 1011 1000 0011 0100 = 340 282 339 999 999 992 395 853 996 843 190 976 512 Apr 18 22:49 UTC (GMT)
0 - 111 1111 1000 - 1110 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 2 633 339 553 020 970 567 962 849 400 569 860 449 635 708 465 247 519 393 653 760 954 458 974 743 244 643 014 639 284 335 777 454 140 934 376 668 162 178 613 637 579 928 254 117 430 993 547 569 784 757 921 743 814 959 376 340 803 006 977 083 294 940 128 331 827 926 019 805 932 701 691 965 097 885 875 921 115 340 524 080 187 898 981 885 017 246 356 244 603 124 227 235 426 948 969 309 111 664 984 729 845 760 Apr 18 22:44 UTC (GMT)
1 - 100 1100 0111 - 0111 0110 0110 0000 0110 0000 1001 0011 0101 1010 1010 0101 0110 = -2 349 999 212 290 342 694 039 218 688 336 252 332 275 839 940 449 760 595 410 944 Apr 18 22:40 UTC (GMT)
0 - 011 1111 1000 - 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1000 0000 0000 = 0.012 499 999 999 999 289 457 264 239 899 814 128 875 732 421 875 Apr 18 22:37 UTC (GMT)
0 - 111 1111 1110 - 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 90 235 768 683 518 591 462 193 639 459 527 218 074 183 610 075 814 997 889 202 208 706 127 534 535 183 100 634 972 809 905 974 095 229 351 307 162 357 320 493 981 072 208 174 423 968 712 230 057 957 704 785 088 059 274 629 278 183 039 081 387 573 281 730 837 303 598 278 683 293 911 311 337 354 222 681 563 552 335 291 814 438 671 779 259 924 308 473 981 733 723 519 933 963 451 348 325 559 720 143 409 381 376 Apr 18 22:35 UTC (GMT)
0 - 000 1110 1100 - 1000 1010 0110 1011 1101 1000 0000 0000 0000 0000 0000 0000 0000 = 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 892 839 404 563 030 969 718 881 298 740 470 443 655 319 022 170 502 571 233 212 264 204 350 7 Apr 18 22:31 UTC (GMT)
0 - 100 0000 0101 - 1110 1100 0111 1110 0110 1011 0111 0100 1101 1100 1110 0101 1010 = 123.123 456 789 000 016 442 514 606 751 501 560 211 181 640 625 Apr 18 22:25 UTC (GMT)
1 - 100 0000 1000 - 1000 0000 1000 1011 1000 0011 1101 0011 0000 0011 1111 1100 0000 = -769.089 960 457 749 839 406 460 523 605 346 679 687 5 Apr 18 22:18 UTC (GMT)
1 - 000 0000 0000 - 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -0 Apr 18 22:15 UTC (GMT)
1 - 011 1111 1111 - 1000 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -1.558 593 75 Apr 18 22:15 UTC (GMT)
0 - 101 1111 0000 - 0011 0010 0110 1110 1101 0010 0000 0000 0000 0000 0000 0000 0000 = 489 782 495 174 892 015 340 676 163 009 664 577 454 979 428 592 820 463 518 889 232 013 930 708 222 419 668 849 885 574 999 037 720 880 722 750 968 558 598 937 053 311 644 609 996 490 617 558 925 312 Apr 18 22:13 UTC (GMT)
0 - 100 0000 0101 - 0000 1001 0011 0011 0011 0011 0011 0011 0011 0011 0011 0011 0011 = 66.299 999 999 999 997 157 829 056 959 599 256 515 502 929 687 5 Apr 18 22:10 UTC (GMT)
1 - 100 0000 0101 - 0010 0100 0100 0100 0100 0100 0000 0000 0000 0000 0000 0000 0000 = -73.066 665 649 414 062 5 Apr 18 22:08 UTC (GMT)
All base ten decimal numbers converted to 64 bit double precision IEEE 754 binary floating point

How to convert numbers from 64 bit double precision IEEE 754 binary floating point standard to decimal system in base 10

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

  • 1. Identify the elements that make up the binary representation of the number:
    First bit (leftmost) indicates the sign, 1 = negative, 0 = pozitive.
    The next 11 bits contain the exponent.
    The last 52 bits contain the mantissa.
  • 2. Convert the exponent, that is allways a positive integer, from binary (base 2) to decimal (base 10).
  • 3. Adjust the exponent, subtract the excess bits, 2(11 - 1) - 1 = 1,023, that is due to the 11 bit excess/bias notation.
  • 4. Convert the mantissa, that represents the number's fractional part (the excess beyond the number's integer part, comma delimited), from binary (base 2) to decimal (base 10).
  • 5. Put all the numbers into expression to calculate the double precision floating point decimal value:
    (-1)Sign × (1 + Mantissa) × 2(Exponent adjusted)

Example: convert the number 1 - 100 0011 1101 - 1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000 from 64 bit double precision IEEE 754 binary floating point system to base ten decimal (double):

  • 1. Identify the elements that make up the binary representation of the number:
    First bit (leftmost) indicates the sign, 1 = negative, 0 = pozitive.
    The next 11 bits contain the exponent: 100 0011 1101
    The last 52 bits contain the mantissa:
    1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000
  • 2. Convert the exponent, that is allways a positive integer, from binary (base 2) to decimal (base 10):
    100 0011 1101(2) =
    1 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20 =
    1,024 + 0 + 0 + 0 + 0 + 32 + 16 + 8 + 4 + 0 + 1 =
    1,024 + 32 + 16 + 8 + 4 + 1 =
    1,085(10)
  • 3. Adjust the exponent, subtract the excess bits, 2(11 - 1) - 1 = 1,023, that is due to the 11 bit excess/bias notation:
    Exponent adjusted = 1,085 - 1,023 = 62
  • 4. Convert the mantissa, that represents the number's fractional part (the excess beyond the number's integer part, comma delimited), from binary (base 2) to decimal (base 10):
    1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000(2) =
    1 × 2-1 + 0 × 2-2 + 0 × 2-3 + 0 × 2-4 + 0 × 2-5 + 0 × 2-6 + 0 × 2-7 + 0 × 2-8 + 0 × 2-9 + 0 × 2-10 + 1 × 2-11 + 0 × 2-12 + 0 × 2-13 + 0 × 2-14 + 0 × 2-15 + 1 × 2-16 + 0 × 2-17 + 1 × 2-18 + 0 × 2-19 + 0 × 2-20 + 0 × 2-21 + 0 × 2-22 + 0 × 2-23 + 0 × 2-24 + 0 × 2-25 + 1 × 2-26 + 0 × 2-27 + 0 × 2-28 + 1 × 2-29 + 1 × 2-30 + 1 × 2-31 + 0 × 2-32 + 0 × 2-33 + 0 × 2-34 + 0 × 2-35 + 0 × 2-36 + 0 × 2-37 + 1 × 2-38 + 0 × 2-39 + 0 × 2-40 + 0 × 2-41 + 0 × 2-42 + 0 × 2-43 + 0 × 2-44 + 1 × 2-45 + 0 × 2-46 + 1 × 2-47 + 0 × 2-48 + 1 × 2-49 + 0 × 2-50 + 0 × 2-51 + 0 × 2-52 =
    0.5 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0.000 488 281 25 + 0 + 0 + 0 + 0 + 0.000 015 258 789 062 5 + 0 + 0.000 003 814 697 265 625 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0.000 000 014 901 161 193 847 656 25 + 0 + 0 + 0.000 000 001 862 645 149 230 957 031 25 + 0.000 000 000 931 322 574 615 478 515 625 + 0.000 000 000 465 661 287 307 739 257 812 5 + 0 + 0 + 0 + 0 + 0 + 0 + 0.000 000 000 003 637 978 807 091 712 951 660 156 25 + 0 + 0 + 0 + 0 + 0 + 0 + 0.000 000 000 000 028 421 709 430 404 007 434 844 970 703 125 + 0 + 0.000 000 000 000 007 105 427 357 601 001 858 711 242 675 781 25 + 0 + 0.000 000 000 000 001 776 356 839 400 250 464 677 810 668 945 312 5 + 0 + 0 + 0 =
    0.5 + 0.000 488 281 25 + 0.000 015 258 789 062 5 + 0.000 003 814 697 265 625 + 0.000 000 014 901 161 193 847 656 25 + 0.000 000 001 862 645 149 230 957 031 25 + 0.000 000 000 931 322 574 615 478 515 625 + 0.000 000 000 465 661 287 307 739 257 812 5 + 0.000 000 000 003 637 978 807 091 712 951 660 156 25 + 0.000 000 000 000 028 421 709 430 404 007 434 844 970 703 125 + 0.000 000 000 000 007 105 427 357 601 001 858 711 242 675 781 25 + 0.000 000 000 000 001 776 356 839 400 250 464 677 810 668 945 312 5 =
    0.500 507 372 900 793 612 302 550 172 898 918 390 274 047 851 562 5(10)
  • 5. Put all the numbers into expression to calculate the double precision floating point decimal value:
    (-1)Sign × (1 + Mantissa) × 2(Exponent adjusted) =
    (-1)1 × (1 + 0.500 507 372 900 793 612 302 550 172 898 918 390 274 047 851 562 5) × 262 =
    -1.500 507 372 900 793 612 302 550 172 898 918 390 274 047 851 562 5 × 262 =
    -6 919 868 872 153 800 704(10)
  • 1 - 100 0011 1101 - 1000 0000 0010 0001 0100 0000 0100 1110 0000 0100 0000 1010 1000 converted from 64 bit double precision IEEE 754 binary floating point representation to a decimal number (float) in decimal system (in base 10) = -6 919 868 872 153 800 704(10)