Unsigned: Integer ↗ Binary: 11 000 101 011 101 102 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 11 000 101 011 101 102(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;
  • 11 000 101 011 101 102 ÷ 2 = 5 500 050 505 550 551 + 0;
  • 5 500 050 505 550 551 ÷ 2 = 2 750 025 252 775 275 + 1;
  • 2 750 025 252 775 275 ÷ 2 = 1 375 012 626 387 637 + 1;
  • 1 375 012 626 387 637 ÷ 2 = 687 506 313 193 818 + 1;
  • 687 506 313 193 818 ÷ 2 = 343 753 156 596 909 + 0;
  • 343 753 156 596 909 ÷ 2 = 171 876 578 298 454 + 1;
  • 171 876 578 298 454 ÷ 2 = 85 938 289 149 227 + 0;
  • 85 938 289 149 227 ÷ 2 = 42 969 144 574 613 + 1;
  • 42 969 144 574 613 ÷ 2 = 21 484 572 287 306 + 1;
  • 21 484 572 287 306 ÷ 2 = 10 742 286 143 653 + 0;
  • 10 742 286 143 653 ÷ 2 = 5 371 143 071 826 + 1;
  • 5 371 143 071 826 ÷ 2 = 2 685 571 535 913 + 0;
  • 2 685 571 535 913 ÷ 2 = 1 342 785 767 956 + 1;
  • 1 342 785 767 956 ÷ 2 = 671 392 883 978 + 0;
  • 671 392 883 978 ÷ 2 = 335 696 441 989 + 0;
  • 335 696 441 989 ÷ 2 = 167 848 220 994 + 1;
  • 167 848 220 994 ÷ 2 = 83 924 110 497 + 0;
  • 83 924 110 497 ÷ 2 = 41 962 055 248 + 1;
  • 41 962 055 248 ÷ 2 = 20 981 027 624 + 0;
  • 20 981 027 624 ÷ 2 = 10 490 513 812 + 0;
  • 10 490 513 812 ÷ 2 = 5 245 256 906 + 0;
  • 5 245 256 906 ÷ 2 = 2 622 628 453 + 0;
  • 2 622 628 453 ÷ 2 = 1 311 314 226 + 1;
  • 1 311 314 226 ÷ 2 = 655 657 113 + 0;
  • 655 657 113 ÷ 2 = 327 828 556 + 1;
  • 327 828 556 ÷ 2 = 163 914 278 + 0;
  • 163 914 278 ÷ 2 = 81 957 139 + 0;
  • 81 957 139 ÷ 2 = 40 978 569 + 1;
  • 40 978 569 ÷ 2 = 20 489 284 + 1;
  • 20 489 284 ÷ 2 = 10 244 642 + 0;
  • 10 244 642 ÷ 2 = 5 122 321 + 0;
  • 5 122 321 ÷ 2 = 2 561 160 + 1;
  • 2 561 160 ÷ 2 = 1 280 580 + 0;
  • 1 280 580 ÷ 2 = 640 290 + 0;
  • 640 290 ÷ 2 = 320 145 + 0;
  • 320 145 ÷ 2 = 160 072 + 1;
  • 160 072 ÷ 2 = 80 036 + 0;
  • 80 036 ÷ 2 = 40 018 + 0;
  • 40 018 ÷ 2 = 20 009 + 0;
  • 20 009 ÷ 2 = 10 004 + 1;
  • 10 004 ÷ 2 = 5 002 + 0;
  • 5 002 ÷ 2 = 2 501 + 0;
  • 2 501 ÷ 2 = 1 250 + 1;
  • 1 250 ÷ 2 = 625 + 0;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 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 11 000 101 011 101 102(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 000 101 011 101 102(10) = 10 0111 0001 0100 1000 1000 1001 1001 0100 0010 1001 0101 1010 1110(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 11 000 101 011 101 101 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 000 101 011 101 103 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)