Unsigned: Integer ↗ Binary: 1 100 110 010 010 101 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 1 100 110 010 010 101(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;
  • 1 100 110 010 010 101 ÷ 2 = 550 055 005 005 050 + 1;
  • 550 055 005 005 050 ÷ 2 = 275 027 502 502 525 + 0;
  • 275 027 502 502 525 ÷ 2 = 137 513 751 251 262 + 1;
  • 137 513 751 251 262 ÷ 2 = 68 756 875 625 631 + 0;
  • 68 756 875 625 631 ÷ 2 = 34 378 437 812 815 + 1;
  • 34 378 437 812 815 ÷ 2 = 17 189 218 906 407 + 1;
  • 17 189 218 906 407 ÷ 2 = 8 594 609 453 203 + 1;
  • 8 594 609 453 203 ÷ 2 = 4 297 304 726 601 + 1;
  • 4 297 304 726 601 ÷ 2 = 2 148 652 363 300 + 1;
  • 2 148 652 363 300 ÷ 2 = 1 074 326 181 650 + 0;
  • 1 074 326 181 650 ÷ 2 = 537 163 090 825 + 0;
  • 537 163 090 825 ÷ 2 = 268 581 545 412 + 1;
  • 268 581 545 412 ÷ 2 = 134 290 772 706 + 0;
  • 134 290 772 706 ÷ 2 = 67 145 386 353 + 0;
  • 67 145 386 353 ÷ 2 = 33 572 693 176 + 1;
  • 33 572 693 176 ÷ 2 = 16 786 346 588 + 0;
  • 16 786 346 588 ÷ 2 = 8 393 173 294 + 0;
  • 8 393 173 294 ÷ 2 = 4 196 586 647 + 0;
  • 4 196 586 647 ÷ 2 = 2 098 293 323 + 1;
  • 2 098 293 323 ÷ 2 = 1 049 146 661 + 1;
  • 1 049 146 661 ÷ 2 = 524 573 330 + 1;
  • 524 573 330 ÷ 2 = 262 286 665 + 0;
  • 262 286 665 ÷ 2 = 131 143 332 + 1;
  • 131 143 332 ÷ 2 = 65 571 666 + 0;
  • 65 571 666 ÷ 2 = 32 785 833 + 0;
  • 32 785 833 ÷ 2 = 16 392 916 + 1;
  • 16 392 916 ÷ 2 = 8 196 458 + 0;
  • 8 196 458 ÷ 2 = 4 098 229 + 0;
  • 4 098 229 ÷ 2 = 2 049 114 + 1;
  • 2 049 114 ÷ 2 = 1 024 557 + 0;
  • 1 024 557 ÷ 2 = 512 278 + 1;
  • 512 278 ÷ 2 = 256 139 + 0;
  • 256 139 ÷ 2 = 128 069 + 1;
  • 128 069 ÷ 2 = 64 034 + 1;
  • 64 034 ÷ 2 = 32 017 + 0;
  • 32 017 ÷ 2 = 16 008 + 1;
  • 16 008 ÷ 2 = 8 004 + 0;
  • 8 004 ÷ 2 = 4 002 + 0;
  • 4 002 ÷ 2 = 2 001 + 0;
  • 2 001 ÷ 2 = 1 000 + 1;
  • 1 000 ÷ 2 = 500 + 0;
  • 500 ÷ 2 = 250 + 0;
  • 250 ÷ 2 = 125 + 0;
  • 125 ÷ 2 = 62 + 1;
  • 62 ÷ 2 = 31 + 0;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 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 1 100 110 010 010 101(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 100 110 010 010 101(10) = 11 1110 1000 1000 1011 0101 0010 0101 1100 0100 1001 1111 0101(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 1 100 110 010 010 100 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 100 110 010 010 102 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)