18.269 999 999 999 999 573 674 358 543 939 888 477 303 3 Converted to 64 Bit Double Precision IEEE 754 Binary Floating Point Representation Standard

Convert decimal 18.269 999 999 999 999 573 674 358 543 939 888 477 303 3(10) to 64 bit double precision IEEE 754 binary floating point representation standard (1 bit for sign, 11 bits for exponent, 52 bits for mantissa)

What are the steps to convert decimal number
18.269 999 999 999 999 573 674 358 543 939 888 477 303 3(10) to 64 bit double precision IEEE 754 binary floating point representation (1 bit for sign, 11 bits for exponent, 52 bits for mantissa)

1. First, convert to binary (in base 2) the integer part: 18.
Divide the number repeatedly by 2.

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the integer part of the number.

Take all the remainders starting from the bottom of the list constructed above.

18(10) =

1 0010(2)


3. Convert to binary (base 2) the fractional part: 0.269 999 999 999 999 573 674 358 543 939 888 477 303 3.

Multiply it repeatedly by 2.

Keep track of each integer part of the results.

Stop when we get a fractional part that is equal to zero.


  • #) multiplying = integer + fractional part;
  • 1) 0.269 999 999 999 999 573 674 358 543 939 888 477 303 3 × 2 = 0 + 0.539 999 999 999 999 147 348 717 087 879 776 954 606 6;
  • 2) 0.539 999 999 999 999 147 348 717 087 879 776 954 606 6 × 2 = 1 + 0.079 999 999 999 998 294 697 434 175 759 553 909 213 2;
  • 3) 0.079 999 999 999 998 294 697 434 175 759 553 909 213 2 × 2 = 0 + 0.159 999 999 999 996 589 394 868 351 519 107 818 426 4;
  • 4) 0.159 999 999 999 996 589 394 868 351 519 107 818 426 4 × 2 = 0 + 0.319 999 999 999 993 178 789 736 703 038 215 636 852 8;
  • 5) 0.319 999 999 999 993 178 789 736 703 038 215 636 852 8 × 2 = 0 + 0.639 999 999 999 986 357 579 473 406 076 431 273 705 6;
  • 6) 0.639 999 999 999 986 357 579 473 406 076 431 273 705 6 × 2 = 1 + 0.279 999 999 999 972 715 158 946 812 152 862 547 411 2;
  • 7) 0.279 999 999 999 972 715 158 946 812 152 862 547 411 2 × 2 = 0 + 0.559 999 999 999 945 430 317 893 624 305 725 094 822 4;
  • 8) 0.559 999 999 999 945 430 317 893 624 305 725 094 822 4 × 2 = 1 + 0.119 999 999 999 890 860 635 787 248 611 450 189 644 8;
  • 9) 0.119 999 999 999 890 860 635 787 248 611 450 189 644 8 × 2 = 0 + 0.239 999 999 999 781 721 271 574 497 222 900 379 289 6;
  • 10) 0.239 999 999 999 781 721 271 574 497 222 900 379 289 6 × 2 = 0 + 0.479 999 999 999 563 442 543 148 994 445 800 758 579 2;
  • 11) 0.479 999 999 999 563 442 543 148 994 445 800 758 579 2 × 2 = 0 + 0.959 999 999 999 126 885 086 297 988 891 601 517 158 4;
  • 12) 0.959 999 999 999 126 885 086 297 988 891 601 517 158 4 × 2 = 1 + 0.919 999 999 998 253 770 172 595 977 783 203 034 316 8;
  • 13) 0.919 999 999 998 253 770 172 595 977 783 203 034 316 8 × 2 = 1 + 0.839 999 999 996 507 540 345 191 955 566 406 068 633 6;
  • 14) 0.839 999 999 996 507 540 345 191 955 566 406 068 633 6 × 2 = 1 + 0.679 999 999 993 015 080 690 383 911 132 812 137 267 2;
  • 15) 0.679 999 999 993 015 080 690 383 911 132 812 137 267 2 × 2 = 1 + 0.359 999 999 986 030 161 380 767 822 265 624 274 534 4;
  • 16) 0.359 999 999 986 030 161 380 767 822 265 624 274 534 4 × 2 = 0 + 0.719 999 999 972 060 322 761 535 644 531 248 549 068 8;
  • 17) 0.719 999 999 972 060 322 761 535 644 531 248 549 068 8 × 2 = 1 + 0.439 999 999 944 120 645 523 071 289 062 497 098 137 6;
  • 18) 0.439 999 999 944 120 645 523 071 289 062 497 098 137 6 × 2 = 0 + 0.879 999 999 888 241 291 046 142 578 124 994 196 275 2;
  • 19) 0.879 999 999 888 241 291 046 142 578 124 994 196 275 2 × 2 = 1 + 0.759 999 999 776 482 582 092 285 156 249 988 392 550 4;
  • 20) 0.759 999 999 776 482 582 092 285 156 249 988 392 550 4 × 2 = 1 + 0.519 999 999 552 965 164 184 570 312 499 976 785 100 8;
  • 21) 0.519 999 999 552 965 164 184 570 312 499 976 785 100 8 × 2 = 1 + 0.039 999 999 105 930 328 369 140 624 999 953 570 201 6;
  • 22) 0.039 999 999 105 930 328 369 140 624 999 953 570 201 6 × 2 = 0 + 0.079 999 998 211 860 656 738 281 249 999 907 140 403 2;
  • 23) 0.079 999 998 211 860 656 738 281 249 999 907 140 403 2 × 2 = 0 + 0.159 999 996 423 721 313 476 562 499 999 814 280 806 4;
  • 24) 0.159 999 996 423 721 313 476 562 499 999 814 280 806 4 × 2 = 0 + 0.319 999 992 847 442 626 953 124 999 999 628 561 612 8;
  • 25) 0.319 999 992 847 442 626 953 124 999 999 628 561 612 8 × 2 = 0 + 0.639 999 985 694 885 253 906 249 999 999 257 123 225 6;
  • 26) 0.639 999 985 694 885 253 906 249 999 999 257 123 225 6 × 2 = 1 + 0.279 999 971 389 770 507 812 499 999 998 514 246 451 2;
  • 27) 0.279 999 971 389 770 507 812 499 999 998 514 246 451 2 × 2 = 0 + 0.559 999 942 779 541 015 624 999 999 997 028 492 902 4;
  • 28) 0.559 999 942 779 541 015 624 999 999 997 028 492 902 4 × 2 = 1 + 0.119 999 885 559 082 031 249 999 999 994 056 985 804 8;
  • 29) 0.119 999 885 559 082 031 249 999 999 994 056 985 804 8 × 2 = 0 + 0.239 999 771 118 164 062 499 999 999 988 113 971 609 6;
  • 30) 0.239 999 771 118 164 062 499 999 999 988 113 971 609 6 × 2 = 0 + 0.479 999 542 236 328 124 999 999 999 976 227 943 219 2;
  • 31) 0.479 999 542 236 328 124 999 999 999 976 227 943 219 2 × 2 = 0 + 0.959 999 084 472 656 249 999 999 999 952 455 886 438 4;
  • 32) 0.959 999 084 472 656 249 999 999 999 952 455 886 438 4 × 2 = 1 + 0.919 998 168 945 312 499 999 999 999 904 911 772 876 8;
  • 33) 0.919 998 168 945 312 499 999 999 999 904 911 772 876 8 × 2 = 1 + 0.839 996 337 890 624 999 999 999 999 809 823 545 753 6;
  • 34) 0.839 996 337 890 624 999 999 999 999 809 823 545 753 6 × 2 = 1 + 0.679 992 675 781 249 999 999 999 999 619 647 091 507 2;
  • 35) 0.679 992 675 781 249 999 999 999 999 619 647 091 507 2 × 2 = 1 + 0.359 985 351 562 499 999 999 999 999 239 294 183 014 4;
  • 36) 0.359 985 351 562 499 999 999 999 999 239 294 183 014 4 × 2 = 0 + 0.719 970 703 124 999 999 999 999 998 478 588 366 028 8;
  • 37) 0.719 970 703 124 999 999 999 999 998 478 588 366 028 8 × 2 = 1 + 0.439 941 406 249 999 999 999 999 996 957 176 732 057 6;
  • 38) 0.439 941 406 249 999 999 999 999 996 957 176 732 057 6 × 2 = 0 + 0.879 882 812 499 999 999 999 999 993 914 353 464 115 2;
  • 39) 0.879 882 812 499 999 999 999 999 993 914 353 464 115 2 × 2 = 1 + 0.759 765 624 999 999 999 999 999 987 828 706 928 230 4;
  • 40) 0.759 765 624 999 999 999 999 999 987 828 706 928 230 4 × 2 = 1 + 0.519 531 249 999 999 999 999 999 975 657 413 856 460 8;
  • 41) 0.519 531 249 999 999 999 999 999 975 657 413 856 460 8 × 2 = 1 + 0.039 062 499 999 999 999 999 999 951 314 827 712 921 6;
  • 42) 0.039 062 499 999 999 999 999 999 951 314 827 712 921 6 × 2 = 0 + 0.078 124 999 999 999 999 999 999 902 629 655 425 843 2;
  • 43) 0.078 124 999 999 999 999 999 999 902 629 655 425 843 2 × 2 = 0 + 0.156 249 999 999 999 999 999 999 805 259 310 851 686 4;
  • 44) 0.156 249 999 999 999 999 999 999 805 259 310 851 686 4 × 2 = 0 + 0.312 499 999 999 999 999 999 999 610 518 621 703 372 8;
  • 45) 0.312 499 999 999 999 999 999 999 610 518 621 703 372 8 × 2 = 0 + 0.624 999 999 999 999 999 999 999 221 037 243 406 745 6;
  • 46) 0.624 999 999 999 999 999 999 999 221 037 243 406 745 6 × 2 = 1 + 0.249 999 999 999 999 999 999 998 442 074 486 813 491 2;
  • 47) 0.249 999 999 999 999 999 999 998 442 074 486 813 491 2 × 2 = 0 + 0.499 999 999 999 999 999 999 996 884 148 973 626 982 4;
  • 48) 0.499 999 999 999 999 999 999 996 884 148 973 626 982 4 × 2 = 0 + 0.999 999 999 999 999 999 999 993 768 297 947 253 964 8;
  • 49) 0.999 999 999 999 999 999 999 993 768 297 947 253 964 8 × 2 = 1 + 0.999 999 999 999 999 999 999 987 536 595 894 507 929 6;
  • 50) 0.999 999 999 999 999 999 999 987 536 595 894 507 929 6 × 2 = 1 + 0.999 999 999 999 999 999 999 975 073 191 789 015 859 2;
  • 51) 0.999 999 999 999 999 999 999 975 073 191 789 015 859 2 × 2 = 1 + 0.999 999 999 999 999 999 999 950 146 383 578 031 718 4;
  • 52) 0.999 999 999 999 999 999 999 950 146 383 578 031 718 4 × 2 = 1 + 0.999 999 999 999 999 999 999 900 292 767 156 063 436 8;
  • 53) 0.999 999 999 999 999 999 999 900 292 767 156 063 436 8 × 2 = 1 + 0.999 999 999 999 999 999 999 800 585 534 312 126 873 6;

We didn't get any fractional part that was equal to zero. But we had enough iterations (over Mantissa limit) and at least one integer that was different from zero => FULL STOP (Losing precision - the converted number we get in the end will be just a very good approximation of the initial one).


4. Construct the base 2 representation of the fractional part of the number.

Take all the integer parts of the multiplying operations, starting from the top of the constructed list above:


0.269 999 999 999 999 573 674 358 543 939 888 477 303 3(10) =

0.0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1111 1(2)

5. Positive number before normalization:

18.269 999 999 999 999 573 674 358 543 939 888 477 303 3(10) =

1 0010.0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1111 1(2)

6. Normalize the binary representation of the number.

Shift the decimal mark 4 positions to the left, so that only one non zero digit remains to the left of it:


18.269 999 999 999 999 573 674 358 543 939 888 477 303 3(10) =

1 0010.0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1111 1(2) =

1 0010.0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1111 1(2) × 20 =

1.0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1111 1(2) × 24


7. Up to this moment, there are the following elements that would feed into the 64 bit double precision IEEE 754 binary floating point representation:

Sign 0 (a positive number)

Exponent (unadjusted): 4

Mantissa (not normalized):
1.0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1111 1


8. Adjust the exponent.

Use the 11 bit excess/bias notation:


Exponent (adjusted) =

Exponent (unadjusted) + 2(11-1) - 1 =

4 + 2(11-1) - 1 =

(4 + 1 023)(10) =

1 027(10)


9. Convert the adjusted exponent from the decimal (base 10) to 11 bit binary.

Use the same technique of repeatedly dividing by 2:


  • division = quotient + remainder;
  • 1 027 ÷ 2 = 513 + 1;
  • 513 ÷ 2 = 256 + 1;
  • 256 ÷ 2 = 128 + 0;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

10. Construct the base 2 representation of the adjusted exponent.

Take all the remainders starting from the bottom of the list constructed above.


Exponent (adjusted) =

1027(10) =

100 0000 0011(2)


11. Normalize the mantissa.

a) Remove the leading (the leftmost) bit, since it's allways 1, and the decimal point, if the case.

b) Adjust its length to 52 bits, by removing the excess bits, from the right (if any of the excess bits is set on 1, we are losing precision...).


Mantissa (normalized) =

1. 0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100 1 1111 =

0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100


12. The three elements that make up the number's 64 bit double precision IEEE 754 binary floating point representation:

Sign (1 bit) =
0 (a positive number)

Exponent (11 bits) =
100 0000 0011

Mantissa (52 bits) =
0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100


Decimal number 18.269 999 999 999 999 573 674 358 543 939 888 477 303 3 converted to 64 bit double precision IEEE 754 binary floating point representation:

0 - 100 0000 0011 - 0010 0100 0101 0001 1110 1011 1000 0101 0001 1110 1011 1000 0100

» Convert decimal 18.269 999 999 999 999 573 674 358 543 939 888 477 298 7 to 64 bit double precision IEEE 754 binary floating point representation standard

» Calculations Performed by Our Visitors: Decimal Numbers Converted to 64 Bit Double Precision IEEE 754 Binary Floating Point Representation Standard. Data organized on a Monthly Basis

» Month 10, 2026 [October]: Decimal Numbers Converted to 64 Bit Double Precision IEEE 754 Binary Floating Point Representation Standard. Calculations performed during the month of: October - by our visitors

How to convert numbers from the decimal system (base ten) to 64 bit double precision IEEE 754 binary floating point standard

Follow the steps below to convert a base 10 decimal number to 64 bit double precision IEEE 754 binary floating point:

  • 1. If the number to be converted is negative, start with its the positive version.
  • 2. First convert the integer part. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, until we get a quotient that is equal to zero, keeping track of each remainder.
  • 3. Construct the base 2 representation of the positive integer part of the number, by taking all the remainders from the previous operations, starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Then convert the fractional part. Multiply the number repeatedly by 2, until we get a fractional part that is equal to zero, keeping track of each integer part of the results.
  • 5. Construct the base 2 representation of the fractional part of the number, by taking all the integer parts of the multiplying operations, starting from the top of the list constructed above (they should appear in the binary representation, from left to right, in the order they have been calculated).
  • 6. Normalize the binary representation of the number, shifting the decimal mark (the decimal point) "n" positions either to the left, or to the right, so that only one non zero digit remains to the left of the decimal mark.
  • 7. Adjust the exponent in 11 bit excess/bias notation and then convert it from decimal (base 10) to 11 bit binary, by using the same technique of repeatedly dividing by 2, as shown above:
    Exponent (adjusted) = Exponent (unadjusted) + 2(11-1) - 1
  • 8. Normalize mantissa, remove the leading (leftmost) bit, since it's allways '1' (and the decimal mark, if the case) and adjust its length to 52 bits, either by removing the excess bits from the right (losing precision...) or by adding extra bits set on '0' to the right.
  • 9. Sign (it takes 1 bit) is either 1 for a negative or 0 for a positive number.

Example: convert the negative number -31.640 215 from the decimal system (base ten) to 64 bit double precision IEEE 754 binary floating point:

  • 1. Start with the positive version of the number:

    |-31.640 215| = 31.640 215

  • 2. First convert the integer part, 31. Divide it repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder;
    • 31 ÷ 2 = 15 + 1;
    • 15 ÷ 2 = 7 + 1;
    • 7 ÷ 2 = 3 + 1;
    • 3 ÷ 2 = 1 + 1;
    • 1 ÷ 2 = 0 + 1;
    • We have encountered a quotient that is ZERO => FULL STOP
  • 3. Construct the base 2 representation of the integer part of the number by taking all the remainders of the previous dividing operations, starting from the bottom of the list constructed above:

    31(10) = 1 1111(2)

  • 4. Then, convert the fractional part, 0.640 215. Multiply repeatedly by 2, keeping track of each integer part of the results, until we get a fractional part that is equal to zero:
    • #) multiplying = integer + fractional part;
    • 1) 0.640 215 × 2 = 1 + 0.280 43;
    • 2) 0.280 43 × 2 = 0 + 0.560 86;
    • 3) 0.560 86 × 2 = 1 + 0.121 72;
    • 4) 0.121 72 × 2 = 0 + 0.243 44;
    • 5) 0.243 44 × 2 = 0 + 0.486 88;
    • 6) 0.486 88 × 2 = 0 + 0.973 76;
    • 7) 0.973 76 × 2 = 1 + 0.947 52;
    • 8) 0.947 52 × 2 = 1 + 0.895 04;
    • 9) 0.895 04 × 2 = 1 + 0.790 08;
    • 10) 0.790 08 × 2 = 1 + 0.580 16;
    • 11) 0.580 16 × 2 = 1 + 0.160 32;
    • 12) 0.160 32 × 2 = 0 + 0.320 64;
    • 13) 0.320 64 × 2 = 0 + 0.641 28;
    • 14) 0.641 28 × 2 = 1 + 0.282 56;
    • 15) 0.282 56 × 2 = 0 + 0.565 12;
    • 16) 0.565 12 × 2 = 1 + 0.130 24;
    • 17) 0.130 24 × 2 = 0 + 0.260 48;
    • 18) 0.260 48 × 2 = 0 + 0.520 96;
    • 19) 0.520 96 × 2 = 1 + 0.041 92;
    • 20) 0.041 92 × 2 = 0 + 0.083 84;
    • 21) 0.083 84 × 2 = 0 + 0.167 68;
    • 22) 0.167 68 × 2 = 0 + 0.335 36;
    • 23) 0.335 36 × 2 = 0 + 0.670 72;
    • 24) 0.670 72 × 2 = 1 + 0.341 44;
    • 25) 0.341 44 × 2 = 0 + 0.682 88;
    • 26) 0.682 88 × 2 = 1 + 0.365 76;
    • 27) 0.365 76 × 2 = 0 + 0.731 52;
    • 28) 0.731 52 × 2 = 1 + 0.463 04;
    • 29) 0.463 04 × 2 = 0 + 0.926 08;
    • 30) 0.926 08 × 2 = 1 + 0.852 16;
    • 31) 0.852 16 × 2 = 1 + 0.704 32;
    • 32) 0.704 32 × 2 = 1 + 0.408 64;
    • 33) 0.408 64 × 2 = 0 + 0.817 28;
    • 34) 0.817 28 × 2 = 1 + 0.634 56;
    • 35) 0.634 56 × 2 = 1 + 0.269 12;
    • 36) 0.269 12 × 2 = 0 + 0.538 24;
    • 37) 0.538 24 × 2 = 1 + 0.076 48;
    • 38) 0.076 48 × 2 = 0 + 0.152 96;
    • 39) 0.152 96 × 2 = 0 + 0.305 92;
    • 40) 0.305 92 × 2 = 0 + 0.611 84;
    • 41) 0.611 84 × 2 = 1 + 0.223 68;
    • 42) 0.223 68 × 2 = 0 + 0.447 36;
    • 43) 0.447 36 × 2 = 0 + 0.894 72;
    • 44) 0.894 72 × 2 = 1 + 0.789 44;
    • 45) 0.789 44 × 2 = 1 + 0.578 88;
    • 46) 0.578 88 × 2 = 1 + 0.157 76;
    • 47) 0.157 76 × 2 = 0 + 0.315 52;
    • 48) 0.315 52 × 2 = 0 + 0.631 04;
    • 49) 0.631 04 × 2 = 1 + 0.262 08;
    • 50) 0.262 08 × 2 = 0 + 0.524 16;
    • 51) 0.524 16 × 2 = 1 + 0.048 32;
    • 52) 0.048 32 × 2 = 0 + 0.096 64;
    • 53) 0.096 64 × 2 = 0 + 0.193 28;
    • We didn't get any fractional part that was equal to zero. But we had enough iterations (over Mantissa limit = 52) and at least one integer part that was different from zero => FULL STOP (losing precision...).
  • 5. Construct the base 2 representation of the fractional part of the number, by taking all the integer parts of the previous multiplying operations, starting from the top of the constructed list above:

    0.640 215(10) = 0.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2)

  • 6. Summarizing - the positive number before normalization:

    31.640 215(10) = 1 1111.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2)

  • 7. Normalize the binary representation of the number, shifting the decimal mark 4 positions to the left so that only one non-zero digit stays to the left of the decimal mark:

    31.640 215(10) =
    1 1111.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2) =
    1 1111.1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2) × 20 =
    1.1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0(2) × 24

  • 8. Up to this moment, there are the following elements that would feed into the 64 bit double precision IEEE 754 binary floating point representation:

    Sign: 1 (a negative number)

    Exponent (unadjusted): 4

    Mantissa (not-normalized): 1.1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0

  • 9. Adjust the exponent in 11 bit excess/bias notation and then convert it from decimal (base 10) to 11 bit binary (base 2), by using the same technique of repeatedly dividing it by 2, as shown above:

    Exponent (adjusted) = Exponent (unadjusted) + 2(11-1) - 1 = (4 + 1023)(10) = 1027(10) =
    100 0000 0011(2)

  • 10. Normalize mantissa, remove the leading (leftmost) bit, since it's allways '1' (and the decimal sign) and adjust its length to 52 bits, by removing the excess bits, from the right (losing precision...):

    Mantissa (not-normalized): 1.1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100 1010 0

    Mantissa (normalized): 1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100

  • Conclusion:

    Sign (1 bit) = 1 (a negative number)

    Exponent (8 bits) = 100 0000 0011

    Mantissa (52 bits) = 1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100

  • Number -31.640 215, converted from decimal system (base 10) to 64 bit double precision IEEE 754 binary floating point =
    1 - 100 0000 0011 - 1111 1010 0011 1110 0101 0010 0001 0101 0111 0110 1000 1001 1100