Convert 100 001 110 137 to Unsigned Binary (Base 2)

See below how to convert 100 001 110 137(10), the unsigned base 10 decimal system number to base 2 binary equivalent

What are the required steps to convert base 10 decimal system
number 100 001 110 137 to base 2 unsigned binary equivalent?

  • A number written in base ten, or a decimal system number, is a number written using the digits 0 through 9. A number written in base two, or a binary system number, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 100 001 110 137 ÷ 2 = 50 000 555 068 + 1;
  • 50 000 555 068 ÷ 2 = 25 000 277 534 + 0;
  • 25 000 277 534 ÷ 2 = 12 500 138 767 + 0;
  • 12 500 138 767 ÷ 2 = 6 250 069 383 + 1;
  • 6 250 069 383 ÷ 2 = 3 125 034 691 + 1;
  • 3 125 034 691 ÷ 2 = 1 562 517 345 + 1;
  • 1 562 517 345 ÷ 2 = 781 258 672 + 1;
  • 781 258 672 ÷ 2 = 390 629 336 + 0;
  • 390 629 336 ÷ 2 = 195 314 668 + 0;
  • 195 314 668 ÷ 2 = 97 657 334 + 0;
  • 97 657 334 ÷ 2 = 48 828 667 + 0;
  • 48 828 667 ÷ 2 = 24 414 333 + 1;
  • 24 414 333 ÷ 2 = 12 207 166 + 1;
  • 12 207 166 ÷ 2 = 6 103 583 + 0;
  • 6 103 583 ÷ 2 = 3 051 791 + 1;
  • 3 051 791 ÷ 2 = 1 525 895 + 1;
  • 1 525 895 ÷ 2 = 762 947 + 1;
  • 762 947 ÷ 2 = 381 473 + 1;
  • 381 473 ÷ 2 = 190 736 + 1;
  • 190 736 ÷ 2 = 95 368 + 0;
  • 95 368 ÷ 2 = 47 684 + 0;
  • 47 684 ÷ 2 = 23 842 + 0;
  • 23 842 ÷ 2 = 11 921 + 0;
  • 11 921 ÷ 2 = 5 960 + 1;
  • 5 960 ÷ 2 = 2 980 + 0;
  • 2 980 ÷ 2 = 1 490 + 0;
  • 1 490 ÷ 2 = 745 + 0;
  • 745 ÷ 2 = 372 + 1;
  • 372 ÷ 2 = 186 + 0;
  • 186 ÷ 2 = 93 + 0;
  • 93 ÷ 2 = 46 + 1;
  • 46 ÷ 2 = 23 + 0;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 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.

100 001 110 137(10) Base 10 decimal system number converted and written as a base 2 unsigned binary equivalent:

100 001 110 137 (base 10) = 1 0111 0100 1000 1000 0111 1101 1000 0111 1001 (base 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 10 to base 2

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)