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 0000 0100 - 1000 0111 0000 0101 1001 0101 0100 0110 1000 0001 0101 1101 0001 = -48.877 726 126 501 904 957 422 084 407 880 902 290 344 238 281 25 May 28 23:51 UTC (GMT)
1 - 100 0000 0101 - 0100 1101 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -83.25 May 28 23:49 UTC (GMT)
1 - 100 0000 0101 - 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = -80 May 28 23:48 UTC (GMT)
1 - 010 1100 0011 - 1010 1110 0101 0000 0110 1011 0111 1000 0101 1000 1111 1110 1001 = 0 May 28 23:48 UTC (GMT)
0 - 100 0000 0101 - 0011 1001 1100 1100 1000 0000 0000 0000 0000 0000 0000 0000 0000 = 78.449 707 031 25 May 28 23:47 UTC (GMT)
0 - 100 0000 0101 - 0011 1001 1100 1101 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 78.450 195 312 5 May 28 23:47 UTC (GMT)
0 - 100 0000 0101 - 0011 1001 1100 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 78.449 218 75 May 28 23:47 UTC (GMT)
0 - 100 0000 0101 - 0011 1001 1100 1110 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 78.451 171 875 May 28 23:47 UTC (GMT)
0 - 100 0000 0101 - 0011 1001 1101 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 78.453 125 May 28 23:46 UTC (GMT)
0 - 100 0000 0101 - 0011 1001 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 78.437 5 May 28 23:46 UTC (GMT)
0 - 100 0000 0011 - 0111 1011 0010 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 23.695 312 5 May 28 23:43 UTC (GMT)
0 - 100 0000 0011 - 0111 1011 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 = 23.703 125 May 28 23:43 UTC (GMT)
0 - 100 0000 0011 - 1110 1101 0100 0111 1010 1110 0001 0100 0111 1010 1110 0001 0100 = 30.829 999 999 999 998 294 697 434 175 759 553 909 301 757 812 5 May 28 23:43 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)