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

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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 - 111 1111 1111 - 1001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = QNaN, Quiet Not a Number Apr 18 23:15 UTC (GMT)
0 - 111 1111 0000 - 1110 0001 1111 1111 1111 1111 1110 0000 0000 0011 1111 1111 1111 = 10 329 342 932 420 764 619 602 851 503 332 582 973 775 058 453 042 077 815 115 580 669 957 101 221 666 349 642 658 151 599 361 955 710 513 876 610 375 090 045 331 069 173 983 874 578 825 476 037 396 291 823 577 854 012 121 898 365 103 227 479 626 406 999 888 955 530 547 709 916 545 223 409 682 335 993 362 700 011 626 829 104 053 086 219 717 566 698 360 082 410 577 797 259 358 126 317 350 631 805 812 736 Apr 18 23:12 UTC (GMT)
0 - 011 1111 0000 - 1010 0011 0110 1110 0010 1110 1011 0001 1100 0100 0000 0000 0000 = 0.000 049 999 999 999 994 493 293 797 859 223 559 498 786 926 269 531 25 Apr 18 23:09 UTC (GMT)
0 - 100 0000 0111 - 1001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 400 Apr 18 23:09 UTC (GMT)
0 - 001 1110 1010 - 0111 0100 0001 1110 1010 0111 0100 0001 1110 1010 0011 0000 0100 = 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 051 695 775 447 224 549 062 387 455 482 500 032 622 024 300 011 216 666 387 667 463 350 165 396 540 618 412 622 434 339 955 623 870 970 226 915 904 449 073 947 573 193 428 379 534 723 170 911 383 Apr 18 23:04 UTC (GMT)
1 - 100 0001 0100 - 0101 0001 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -2 760 704 Apr 18 23:00 UTC (GMT)
0 - 100 0000 0010 - 0110 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 11.375 Apr 18 22:58 UTC (GMT)
1 - 110 1001 1010 - 1110 1110 0011 0111 1111 1001 1011 1100 1010 0101 0000 0100 0000 = -1 182 187 264 655 882 769 725 012 800 394 836 603 681 683 239 498 641 708 016 610 544 405 367 665 970 036 204 305 049 632 848 236 883 867 101 788 696 195 330 520 708 943 956 353 105 328 402 916 991 106 218 806 078 417 752 973 721 598 100 322 912 645 561 487 154 216 960 Apr 18 22:54 UTC (GMT)
0 - 100 0001 0101 - 0110 0101 0001 0010 0101 0111 0100 1001 1000 1010 0011 0001 1001 = 5 850 261.821 816 229 261 457 920 074 462 890 625 Apr 18 22:53 UTC (GMT)
0 - 100 0001 0000 - 0111 1101 1101 0101 1001 0101 1100 0010 1000 1010 0000 1000 1100 = 195 499.169 999 365 112 744 271 755 218 505 859 375 Apr 18 22:52 UTC (GMT)
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)
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)