Unsigned: Integer ↗ Binary: 1 000 010 100 111 111 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 1 000 010 100 111 111(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;
  • 1 000 010 100 111 111 ÷ 2 = 500 005 050 055 555 + 1;
  • 500 005 050 055 555 ÷ 2 = 250 002 525 027 777 + 1;
  • 250 002 525 027 777 ÷ 2 = 125 001 262 513 888 + 1;
  • 125 001 262 513 888 ÷ 2 = 62 500 631 256 944 + 0;
  • 62 500 631 256 944 ÷ 2 = 31 250 315 628 472 + 0;
  • 31 250 315 628 472 ÷ 2 = 15 625 157 814 236 + 0;
  • 15 625 157 814 236 ÷ 2 = 7 812 578 907 118 + 0;
  • 7 812 578 907 118 ÷ 2 = 3 906 289 453 559 + 0;
  • 3 906 289 453 559 ÷ 2 = 1 953 144 726 779 + 1;
  • 1 953 144 726 779 ÷ 2 = 976 572 363 389 + 1;
  • 976 572 363 389 ÷ 2 = 488 286 181 694 + 1;
  • 488 286 181 694 ÷ 2 = 244 143 090 847 + 0;
  • 244 143 090 847 ÷ 2 = 122 071 545 423 + 1;
  • 122 071 545 423 ÷ 2 = 61 035 772 711 + 1;
  • 61 035 772 711 ÷ 2 = 30 517 886 355 + 1;
  • 30 517 886 355 ÷ 2 = 15 258 943 177 + 1;
  • 15 258 943 177 ÷ 2 = 7 629 471 588 + 1;
  • 7 629 471 588 ÷ 2 = 3 814 735 794 + 0;
  • 3 814 735 794 ÷ 2 = 1 907 367 897 + 0;
  • 1 907 367 897 ÷ 2 = 953 683 948 + 1;
  • 953 683 948 ÷ 2 = 476 841 974 + 0;
  • 476 841 974 ÷ 2 = 238 420 987 + 0;
  • 238 420 987 ÷ 2 = 119 210 493 + 1;
  • 119 210 493 ÷ 2 = 59 605 246 + 1;
  • 59 605 246 ÷ 2 = 29 802 623 + 0;
  • 29 802 623 ÷ 2 = 14 901 311 + 1;
  • 14 901 311 ÷ 2 = 7 450 655 + 1;
  • 7 450 655 ÷ 2 = 3 725 327 + 1;
  • 3 725 327 ÷ 2 = 1 862 663 + 1;
  • 1 862 663 ÷ 2 = 931 331 + 1;
  • 931 331 ÷ 2 = 465 665 + 1;
  • 465 665 ÷ 2 = 232 832 + 1;
  • 232 832 ÷ 2 = 116 416 + 0;
  • 116 416 ÷ 2 = 58 208 + 0;
  • 58 208 ÷ 2 = 29 104 + 0;
  • 29 104 ÷ 2 = 14 552 + 0;
  • 14 552 ÷ 2 = 7 276 + 0;
  • 7 276 ÷ 2 = 3 638 + 0;
  • 3 638 ÷ 2 = 1 819 + 0;
  • 1 819 ÷ 2 = 909 + 1;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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 1 000 010 100 111 111(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 000 010 100 111 111(10) = 11 1000 1101 1000 0000 1111 1110 1100 1001 1111 0111 0000 0111(2)

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

The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)

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)