Unsigned: Integer ↗ Binary: 123 456 789 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 123 456 789(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;
  • 123 456 789 ÷ 2 = 61 728 394 + 1;
  • 61 728 394 ÷ 2 = 30 864 197 + 0;
  • 30 864 197 ÷ 2 = 15 432 098 + 1;
  • 15 432 098 ÷ 2 = 7 716 049 + 0;
  • 7 716 049 ÷ 2 = 3 858 024 + 1;
  • 3 858 024 ÷ 2 = 1 929 012 + 0;
  • 1 929 012 ÷ 2 = 964 506 + 0;
  • 964 506 ÷ 2 = 482 253 + 0;
  • 482 253 ÷ 2 = 241 126 + 1;
  • 241 126 ÷ 2 = 120 563 + 0;
  • 120 563 ÷ 2 = 60 281 + 1;
  • 60 281 ÷ 2 = 30 140 + 1;
  • 30 140 ÷ 2 = 15 070 + 0;
  • 15 070 ÷ 2 = 7 535 + 0;
  • 7 535 ÷ 2 = 3 767 + 1;
  • 3 767 ÷ 2 = 1 883 + 1;
  • 1 883 ÷ 2 = 941 + 1;
  • 941 ÷ 2 = 470 + 1;
  • 470 ÷ 2 = 235 + 0;
  • 235 ÷ 2 = 117 + 1;
  • 117 ÷ 2 = 58 + 1;
  • 58 ÷ 2 = 29 + 0;
  • 29 ÷ 2 = 14 + 1;
  • 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 123 456 789(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

123 456 789(10) = 111 0101 1011 1100 1101 0001 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 123 456 788 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 123 456 790 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)