# Convert the Base Ten Unsigned Number 582 To Base Two Binary Code. The Natural Number (a Positive Integer - No Sign) Converted From Decimal System and Written As Binary Code

## Base ten unsigned number 582(10) converted and written as a base two binary code

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

#### Stop when getting a quotient that is equal to zero.

• division = quotient + remainder;
• 582 ÷ 2 = 291 + 0;
• 291 ÷ 2 = 145 + 1;
• 145 ÷ 2 = 72 + 1;
• 72 ÷ 2 = 36 + 0;
• 36 ÷ 2 = 18 + 0;
• 18 ÷ 2 = 9 + 0;
• 9 ÷ 2 = 4 + 1;
• 4 ÷ 2 = 2 + 0;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;

## 582(10) = 10 0100 0110(2)

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

## 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)