Unsigned: Integer ↗ Binary: 12 345 678 987 654 329 Convert the Positive Integer (Whole Number) From Base Ten (10) To Base Two (2), Conversion and Writing of Decimal System Number as Unsigned Binary Code

Unsigned (positive) integer number 12 345 678 987 654 329(10)
converted and written as an unsigned binary (base 2) = ?

1. 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;
  • 12 345 678 987 654 329 ÷ 2 = 6 172 839 493 827 164 + 1;
  • 6 172 839 493 827 164 ÷ 2 = 3 086 419 746 913 582 + 0;
  • 3 086 419 746 913 582 ÷ 2 = 1 543 209 873 456 791 + 0;
  • 1 543 209 873 456 791 ÷ 2 = 771 604 936 728 395 + 1;
  • 771 604 936 728 395 ÷ 2 = 385 802 468 364 197 + 1;
  • 385 802 468 364 197 ÷ 2 = 192 901 234 182 098 + 1;
  • 192 901 234 182 098 ÷ 2 = 96 450 617 091 049 + 0;
  • 96 450 617 091 049 ÷ 2 = 48 225 308 545 524 + 1;
  • 48 225 308 545 524 ÷ 2 = 24 112 654 272 762 + 0;
  • 24 112 654 272 762 ÷ 2 = 12 056 327 136 381 + 0;
  • 12 056 327 136 381 ÷ 2 = 6 028 163 568 190 + 1;
  • 6 028 163 568 190 ÷ 2 = 3 014 081 784 095 + 0;
  • 3 014 081 784 095 ÷ 2 = 1 507 040 892 047 + 1;
  • 1 507 040 892 047 ÷ 2 = 753 520 446 023 + 1;
  • 753 520 446 023 ÷ 2 = 376 760 223 011 + 1;
  • 376 760 223 011 ÷ 2 = 188 380 111 505 + 1;
  • 188 380 111 505 ÷ 2 = 94 190 055 752 + 1;
  • 94 190 055 752 ÷ 2 = 47 095 027 876 + 0;
  • 47 095 027 876 ÷ 2 = 23 547 513 938 + 0;
  • 23 547 513 938 ÷ 2 = 11 773 756 969 + 0;
  • 11 773 756 969 ÷ 2 = 5 886 878 484 + 1;
  • 5 886 878 484 ÷ 2 = 2 943 439 242 + 0;
  • 2 943 439 242 ÷ 2 = 1 471 719 621 + 0;
  • 1 471 719 621 ÷ 2 = 735 859 810 + 1;
  • 735 859 810 ÷ 2 = 367 929 905 + 0;
  • 367 929 905 ÷ 2 = 183 964 952 + 1;
  • 183 964 952 ÷ 2 = 91 982 476 + 0;
  • 91 982 476 ÷ 2 = 45 991 238 + 0;
  • 45 991 238 ÷ 2 = 22 995 619 + 0;
  • 22 995 619 ÷ 2 = 11 497 809 + 1;
  • 11 497 809 ÷ 2 = 5 748 904 + 1;
  • 5 748 904 ÷ 2 = 2 874 452 + 0;
  • 2 874 452 ÷ 2 = 1 437 226 + 0;
  • 1 437 226 ÷ 2 = 718 613 + 0;
  • 718 613 ÷ 2 = 359 306 + 1;
  • 359 306 ÷ 2 = 179 653 + 0;
  • 179 653 ÷ 2 = 89 826 + 1;
  • 89 826 ÷ 2 = 44 913 + 0;
  • 44 913 ÷ 2 = 22 456 + 1;
  • 22 456 ÷ 2 = 11 228 + 0;
  • 11 228 ÷ 2 = 5 614 + 0;
  • 5 614 ÷ 2 = 2 807 + 0;
  • 2 807 ÷ 2 = 1 403 + 1;
  • 1 403 ÷ 2 = 701 + 1;
  • 701 ÷ 2 = 350 + 1;
  • 350 ÷ 2 = 175 + 0;
  • 175 ÷ 2 = 87 + 1;
  • 87 ÷ 2 = 43 + 1;
  • 43 ÷ 2 = 21 + 1;
  • 21 ÷ 2 = 10 + 1;
  • 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 12 345 678 987 654 329(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

12 345 678 987 654 329(10) = 10 1011 1101 1100 0101 0100 0110 0010 1001 0001 1111 0100 1011 1001(2)

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

More operations on unsigned integer numbers:

» Unsigned (positive) integer number 12 345 678 987 654 328 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 12 345 678 987 654 330 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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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)