Converter from 64 bit double precision IEEE 754 binary floating point standard system: converting to base ten decimal numbers (double)

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

Entered binary numbers length must be as indicated - or else extra bits of '0' value will be added to the end (to the right).

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

1 - 100 0100 1111 - 1001 0001 0101 1001 0101 0001 0101 0010 1010 1010 0001 1011 0101 = -1 895 316 579 786 387 326 238 720 Feb 21 13:40 UTC (GMT)
1 - 100 1010 1110 - 1001 0101 1000 0101 0101 0010 0000 0101 0101 0111 1110 1010 1010 = -75 861 668 866 319 282 910 687 601 504 749 216 720 588 443 188 461 568 Feb 21 13:28 UTC (GMT)
0 - 100 0011 0100 - 0111 0001 1000 1110 0000 0000 0000 0010 0000 0000 0000 0000 0100 = 13 002 549 636 366 344 Feb 21 13:09 UTC (GMT)
0 - 101 0000 0000 - 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 347 376 267 711 948 586 270 712 955 026 063 723 559 809 953 996 921 692 118 372 752 023 739 388 919 808 Feb 21 12:51 UTC (GMT)
0 - 000 0000 0000 - 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 0 Feb 21 12:19 UTC (GMT)
0 - 100 0001 0000 - 0001 1101 0001 0111 0111 0101 1100 1101 0101 0111 0011 0110 0100 = 145 966.920 328 999 985 940 754 413 604 736 328 125 Feb 21 12:17 UTC (GMT)
1 - 100 0000 0100 - 1000 0001 0101 1111 0101 0100 0010 1011 1011 0100 0000 0111 1101 = -48.171 547 261 649 699 578 356 376 150 622 963 905 334 472 656 25 Feb 21 11:15 UTC (GMT)
0 - 100 0000 0111 - 0000 1100 0011 1010 1110 0001 0100 0111 1010 1110 0000 0000 0000 = 268.229 999 999 981 373 548 507 690 429 687 5 Feb 21 10:49 UTC (GMT)
1 - 100 0010 0011 - 0110 0110 0110 0011 0000 0000 0111 0011 0101 1010 1010 0101 0110 = -96 203 704 117.665 374 755 859 375 Feb 21 08:22 UTC (GMT)
1 - 100 0001 0001 - 1110 0111 0100 0000 0000 0010 0010 1011 0110 1000 0110 1111 0101 = -498 944.033 899 410 918 820 649 385 452 270 507 812 5 Feb 21 07:46 UTC (GMT)
0 - 000 0000 0000 - 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1110 = 0 Feb 21 06:27 UTC (GMT)
1 - 111 1001 0101 - 1011 1111 1100 0110 0001 0000 1111 0110 0000 0000 0000 0000 0000 = -3 875 739 974 753 834 706 075 163 486 913 256 793 856 570 234 510 836 280 412 770 513 148 715 349 080 425 257 484 493 363 182 218 688 710 603 984 309 181 221 006 228 382 042 997 444 461 286 993 983 555 596 632 805 592 952 453 024 263 932 572 099 783 602 225 529 645 252 313 717 991 116 420 093 794 541 292 813 610 327 893 705 685 088 582 916 171 632 511 843 259 383 808 Feb 21 06:04 UTC (GMT)
1 - 100 0010 0011 - 0110 0110 0110 0011 0000 0000 0111 0011 0101 1010 1010 0101 0110 = -96 203 704 117.665 374 755 859 375 Feb 21 05:37 UTC (GMT)

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 to base 10 decimal system:

  • 1. View 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 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 to decimal number (double) in decimal system (in base 10):

  • 1. View 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 to decimal number (float) in decimal system (in base 10) = -6 919 868 872 153 800 704(10)