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

0 - 101 1111 0000 - 0011 0010 0110 1110 1101 1000 0000 0000 0000 0000 0000 0000 0000 = 489 782 641 506 855 311 402 812 009 022 034 724 009 650 010 558 358 400 939 411 928 536 913 190 661 719 926 026 399 018 138 386 301 981 908 899 085 445 995 252 988 759 868 733 856 457 255 932 657 664 Jul 24 15:57 UTC (GMT)
0 - 100 0001 1010 - 0111 0000 0101 1011 0101 1011 0101 1011 0001 1110 0000 0000 0000 = 193 125 082.847 412 109 375 Jul 24 15:54 UTC (GMT)
0 - 001 1111 1110 - 0010 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 0 Jul 24 15:50 UTC (GMT)
1 - 001 1101 0111 - 1000 0010 0000 0011 0100 0000 0000 0010 0001 0000 0000 0000 0001 = 0 Jul 24 15:25 UTC (GMT)
1 - 011 1110 0000 - 0111 1000 0010 1010 0111 0100 1001 1110 0000 0111 1111 1111 1010 = -0.000 000 000 684 241 680 462 814 526 618 670 319 627 491 666 070 184 8 Jul 24 15:20 UTC (GMT)
0 - 101 1111 0000 - 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 613 760 738 980 526 600 627 473 068 155 174 841 040 620 383 633 074 648 028 117 131 518 025 086 825 876 479 040 613 142 311 107 029 465 791 253 273 917 513 314 228 235 602 353 511 197 499 098 923 008 Jul 24 15:15 UTC (GMT)
0 - 100 0001 0100 - 1011 1000 0011 0101 1001 1011 0110 0110 0111 0100 1010 1001 0100 = 3 606 195.425 027 200 952 172 279 357 910 156 25 Jul 24 15:01 UTC (GMT)
0 - 100 0000 0111 - 1000 0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1001 = 386.270 000 000 000 038 653 524 825 349 450 111 389 160 156 25 Jul 24 15:00 UTC (GMT)
0 - 100 0000 1000 - 0000 1010 0011 0000 1000 0011 0001 0010 0110 1110 1001 0111 1000 = 532.378 999 999 999 905 412 551 015 615 463 256 835 937 5 Jul 24 14:58 UTC (GMT)
0 - 000 0011 1000 - 0000 0000 0000 0011 1111 1000 0000 0000 0000 0000 0000 0000 0000 = 0 Jul 24 14:55 UTC (GMT)
0 - 100 0001 0110 - 0000 0010 1111 1111 0000 1010 0001 0111 0000 0101 1001 1101 0110 = 8 486 789.044 964 712 113 142 013 549 804 687 5 Jul 24 14:48 UTC (GMT)
0 - 100 0011 0011 - 1011 0110 0011 0111 0101 0101 0011 0010 1011 0010 1011 0100 0011 = 7 709 179 928 849 219 Jul 24 14:47 UTC (GMT)
0 - 011 1111 1111 - 1011 0011 0011 0011 0011 0011 0011 0011 0011 0011 0011 0011 0011 = 1.699 999 999 999 999 955 591 079 014 993 738 383 054 733 276 367 187 5 Jul 24 14:41 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)