# Convert the Positive Integer (Whole Number) 110 010 100 118 From Base Ten (10) To Base Two (2): Conversion and Writing of the Decimal System Number as an Unsigned Binary Code

## Unsigned (positive) integer number 110 010 100 118(10) converted and written as an unsigned binary (base 2) = ?

### 1. Divide the number repeatedly by 2:

#### We stop when we get a quotient that is equal to zero.

• division = quotient + remainder;
• 110 010 100 118 ÷ 2 = 55 005 050 059 + 0;
• 55 005 050 059 ÷ 2 = 27 502 525 029 + 1;
• 27 502 525 029 ÷ 2 = 13 751 262 514 + 1;
• 13 751 262 514 ÷ 2 = 6 875 631 257 + 0;
• 6 875 631 257 ÷ 2 = 3 437 815 628 + 1;
• 3 437 815 628 ÷ 2 = 1 718 907 814 + 0;
• 1 718 907 814 ÷ 2 = 859 453 907 + 0;
• 859 453 907 ÷ 2 = 429 726 953 + 1;
• 429 726 953 ÷ 2 = 214 863 476 + 1;
• 214 863 476 ÷ 2 = 107 431 738 + 0;
• 107 431 738 ÷ 2 = 53 715 869 + 0;
• 53 715 869 ÷ 2 = 26 857 934 + 1;
• 26 857 934 ÷ 2 = 13 428 967 + 0;
• 13 428 967 ÷ 2 = 6 714 483 + 1;
• 6 714 483 ÷ 2 = 3 357 241 + 1;
• 3 357 241 ÷ 2 = 1 678 620 + 1;
• 1 678 620 ÷ 2 = 839 310 + 0;
• 839 310 ÷ 2 = 419 655 + 0;
• 419 655 ÷ 2 = 209 827 + 1;
• 209 827 ÷ 2 = 104 913 + 1;
• 104 913 ÷ 2 = 52 456 + 1;
• 52 456 ÷ 2 = 26 228 + 0;
• 26 228 ÷ 2 = 13 114 + 0;
• 13 114 ÷ 2 = 6 557 + 0;
• 6 557 ÷ 2 = 3 278 + 1;
• 3 278 ÷ 2 = 1 639 + 0;
• 1 639 ÷ 2 = 819 + 1;
• 819 ÷ 2 = 409 + 1;
• 409 ÷ 2 = 204 + 1;
• 204 ÷ 2 = 102 + 0;
• 102 ÷ 2 = 51 + 0;
• 51 ÷ 2 = 25 + 1;
• 25 ÷ 2 = 12 + 1;
• 12 ÷ 2 = 6 + 0;
• 6 ÷ 2 = 3 + 0;
• 3 ÷ 2 = 1 + 1;
• 1 ÷ 2 = 0 + 1;

## 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)