# Unsigned: Integer -> Binary: 111 011 009 995 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 111 011 009 995_{(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**; - 111 011 009 995 ÷ 2 = 55 505 504 997 +
**1**; - 55 505 504 997 ÷ 2 = 27 752 752 498 +
**1**; - 27 752 752 498 ÷ 2 = 13 876 376 249 +
**0**; - 13 876 376 249 ÷ 2 = 6 938 188 124 +
**1**; - 6 938 188 124 ÷ 2 = 3 469 094 062 +
**0**; - 3 469 094 062 ÷ 2 = 1 734 547 031 +
**0**; - 1 734 547 031 ÷ 2 = 867 273 515 +
**1**; - 867 273 515 ÷ 2 = 433 636 757 +
**1**; - 433 636 757 ÷ 2 = 216 818 378 +
**1**; - 216 818 378 ÷ 2 = 108 409 189 +
**0**; - 108 409 189 ÷ 2 = 54 204 594 +
**1**; - 54 204 594 ÷ 2 = 27 102 297 +
**0**; - 27 102 297 ÷ 2 = 13 551 148 +
**1**; - 13 551 148 ÷ 2 = 6 775 574 +
**0**; - 6 775 574 ÷ 2 = 3 387 787 +
**0**; - 3 387 787 ÷ 2 = 1 693 893 +
**1**; - 1 693 893 ÷ 2 = 846 946 +
**1**; - 846 946 ÷ 2 = 423 473 +
**0**; - 423 473 ÷ 2 = 211 736 +
**1**; - 211 736 ÷ 2 = 105 868 +
**0**; - 105 868 ÷ 2 = 52 934 +
**0**; - 52 934 ÷ 2 = 26 467 +
**0**; - 26 467 ÷ 2 = 13 233 +
**1**; - 13 233 ÷ 2 = 6 616 +
**1**; - 6 616 ÷ 2 = 3 308 +
**0**; - 3 308 ÷ 2 = 1 654 +
**0**; - 1 654 ÷ 2 = 827 +
**0**; - 827 ÷ 2 = 413 +
**1**; - 413 ÷ 2 = 206 +
**1**; - 206 ÷ 2 = 103 +
**0**; - 103 ÷ 2 = 51 +
**1**; - 51 ÷ 2 = 25 +
**1**; - 25 ÷ 2 = 12 +
**1**; - 12 ÷ 2 = 6 +
**0**; - 6 ÷ 2 = 3 +
**0**; - 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 111 011 009 995_{(10)}, a positive integer number (with no sign),

converted from decimal system (from base 10)

and written as an unsigned binary (in base 2):

## 111 011 009 995_{(10)} = 1 1001 1101 1000 1100 0101 1001 0101 1100 1011_{(2)}

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

## Convert positive integer numbers (unsigned) from decimal system (base ten) to binary (base two)

### How to convert a base 10 positive integer number to base 2:

#### 1) Divide the number repeatedly by 2, keeping track of each remainder, until getting a quotient that is 0;

#### 2) Construct the base 2 representation by taking all the previously calculated remainders starting from the last remainder up to the first one, in that order.