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 - 101 1000 0000 - 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1100 0000 0000 = 118 206 018 589 237 191 510 649 387 601 484 220 029 972 860 474 071 259 495 778 511 801 574 765 052 914 762 839 151 122 627 343 887 982 258 402 541 699 072 Jun 26 11:59 UTC (GMT)
0 - 100 0001 1010 - 0111 1111 0011 0110 1101 1111 1110 0011 1010 0011 1111 0110 0001 = 200 914 687.113 764 792 680 740 356 445 312 5 Jun 26 11:54 UTC (GMT)
1 - 010 0111 0110 - 0001 1110 1011 0000 1111 1001 0101 1001 0000 0000 0000 0000 0000 = -0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 055 511 921 440 323 333 013 016 074 340 048 252 840 475 408 469 223 877 021 642 072 767 056 829 390 757 962 520 935 892 113 808 609 957 008 119 817 758 072 196 011 866 219 803 876 048 254 209 312 308 982 449 725 983 691 592 101 954 366 737 427 768 053 6 Jun 26 11:53 UTC (GMT)
0 - 000 0000 0000 - 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 0 Jun 26 11:53 UTC (GMT)
0 - 011 1111 1100 - 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 = 0.199 999 999 999 999 983 346 654 630 622 651 893 645 524 978 637 695 312 5 Jun 26 11:50 UTC (GMT)
0 - 100 0000 0100 - 1001 0010 1010 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 50.333 984 375 Jun 26 11:48 UTC (GMT)
0 - 011 1111 1010 - 0000 0111 1100 1000 0100 1011 0101 1101 1100 1100 0110 0011 1111 = 0.032 199 999 999 999 999 455 990 717 933 673 295 192 420 482 635 498 046 875 Jun 26 11:36 UTC (GMT)
0 - 100 0000 0100 - 0101 0010 0001 1100 1010 1100 0000 1000 0011 0001 0010 0110 1111 = 42.264 000 000 000 002 899 014 361 901 208 758 354 187 011 718 75 Jun 26 11:35 UTC (GMT)
1 - 100 0000 0110 - 1101 0011 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -233.75 Jun 26 11:32 UTC (GMT)
1 - 101 0100 0101 - 1000 0101 0101 0000 0101 0101 0111 1110 0000 0000 1111 0101 0101 = -207 892 309 833 255 498 987 547 816 648 997 430 273 358 774 279 772 270 680 065 363 208 053 040 712 265 028 215 618 950 198 722 560 Jun 26 11:27 UTC (GMT)
1 - 100 0000 0010 - 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -10 Jun 26 11:19 UTC (GMT)
1 - 011 1111 1110 - 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -0.75 Jun 26 11:18 UTC (GMT)
0 - 100 0000 0100 - 1011 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 54 Jun 26 11:15 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)