# Unsigned: Integer -> Binary: 15 765 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 15 765(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;
• 15 765 ÷ 2 = 7 882 + 1;
• 7 882 ÷ 2 = 3 941 + 0;
• 3 941 ÷ 2 = 1 970 + 1;
• 1 970 ÷ 2 = 985 + 0;
• 985 ÷ 2 = 492 + 1;
• 492 ÷ 2 = 246 + 0;
• 246 ÷ 2 = 123 + 0;
• 123 ÷ 2 = 61 + 1;
• 61 ÷ 2 = 30 + 1;
• 30 ÷ 2 = 15 + 0;
• 15 ÷ 2 = 7 + 1;
• 7 ÷ 2 = 3 + 1;
• 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)