Base Ten to Base Two: Unsigned Number 738 477 384 737 883 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 738 477 384 737 883(10) converted and written as a base two binary code

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when getting a quotient that is equal to zero.


  • division = quotient + remainder;
  • 738 477 384 737 883 ÷ 2 = 369 238 692 368 941 + 1;
  • 369 238 692 368 941 ÷ 2 = 184 619 346 184 470 + 1;
  • 184 619 346 184 470 ÷ 2 = 92 309 673 092 235 + 0;
  • 92 309 673 092 235 ÷ 2 = 46 154 836 546 117 + 1;
  • 46 154 836 546 117 ÷ 2 = 23 077 418 273 058 + 1;
  • 23 077 418 273 058 ÷ 2 = 11 538 709 136 529 + 0;
  • 11 538 709 136 529 ÷ 2 = 5 769 354 568 264 + 1;
  • 5 769 354 568 264 ÷ 2 = 2 884 677 284 132 + 0;
  • 2 884 677 284 132 ÷ 2 = 1 442 338 642 066 + 0;
  • 1 442 338 642 066 ÷ 2 = 721 169 321 033 + 0;
  • 721 169 321 033 ÷ 2 = 360 584 660 516 + 1;
  • 360 584 660 516 ÷ 2 = 180 292 330 258 + 0;
  • 180 292 330 258 ÷ 2 = 90 146 165 129 + 0;
  • 90 146 165 129 ÷ 2 = 45 073 082 564 + 1;
  • 45 073 082 564 ÷ 2 = 22 536 541 282 + 0;
  • 22 536 541 282 ÷ 2 = 11 268 270 641 + 0;
  • 11 268 270 641 ÷ 2 = 5 634 135 320 + 1;
  • 5 634 135 320 ÷ 2 = 2 817 067 660 + 0;
  • 2 817 067 660 ÷ 2 = 1 408 533 830 + 0;
  • 1 408 533 830 ÷ 2 = 704 266 915 + 0;
  • 704 266 915 ÷ 2 = 352 133 457 + 1;
  • 352 133 457 ÷ 2 = 176 066 728 + 1;
  • 176 066 728 ÷ 2 = 88 033 364 + 0;
  • 88 033 364 ÷ 2 = 44 016 682 + 0;
  • 44 016 682 ÷ 2 = 22 008 341 + 0;
  • 22 008 341 ÷ 2 = 11 004 170 + 1;
  • 11 004 170 ÷ 2 = 5 502 085 + 0;
  • 5 502 085 ÷ 2 = 2 751 042 + 1;
  • 2 751 042 ÷ 2 = 1 375 521 + 0;
  • 1 375 521 ÷ 2 = 687 760 + 1;
  • 687 760 ÷ 2 = 343 880 + 0;
  • 343 880 ÷ 2 = 171 940 + 0;
  • 171 940 ÷ 2 = 85 970 + 0;
  • 85 970 ÷ 2 = 42 985 + 0;
  • 42 985 ÷ 2 = 21 492 + 1;
  • 21 492 ÷ 2 = 10 746 + 0;
  • 10 746 ÷ 2 = 5 373 + 0;
  • 5 373 ÷ 2 = 2 686 + 1;
  • 2 686 ÷ 2 = 1 343 + 0;
  • 1 343 ÷ 2 = 671 + 1;
  • 671 ÷ 2 = 335 + 1;
  • 335 ÷ 2 = 167 + 1;
  • 167 ÷ 2 = 83 + 1;
  • 83 ÷ 2 = 41 + 1;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

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

Number 738 477 384 737 883(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

738 477 384 737 883(10) = 10 1001 1111 1010 0100 0010 1010 0011 0001 0010 0100 0101 1011(2)

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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How to convert unsigned integer numbers (positive) from decimal system (base 10) to binary = simply convert from base ten to base two

Follow the steps below to convert a base ten unsigned integer number to base two:

  • 1. Divide repeatedly by 2 the positive integer number that has to be converted to binary, keeping track of each remainder, until we get a QUOTIENT that is equal to ZERO.
  • 2. Construct the base 2 representation of the positive integer number, by taking all the remainders 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).

Example: convert the positive integer number 55 from decimal system (base ten) to binary code (base two):

  • 1. Divide repeatedly 55 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder;
    • 55 ÷ 2 = 27 + 1;
    • 27 ÷ 2 = 13 + 1;
    • 13 ÷ 2 = 6 + 1;
    • 6 ÷ 2 = 3 + 0;
    • 3 ÷ 2 = 1 + 1;
    • 1 ÷ 2 = 0 + 1;
  • 2. Construct the base 2 representation of the positive integer number, by taking all the remainders starting from the bottom of the list constructed above:
  • 55(10) = 11 0111(2)
  • Number 5510, positive integer (no sign), converted from decimal system (base 10) to unsigned binary (base 2) = 11 0111(2)