### 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**; - 1 111 111 111 111 208 ÷ 2 = 555 555 555 555 604 +
**0**; - 555 555 555 555 604 ÷ 2 = 277 777 777 777 802 +
**0**; - 277 777 777 777 802 ÷ 2 = 138 888 888 888 901 +
**0**; - 138 888 888 888 901 ÷ 2 = 69 444 444 444 450 +
**1**; - 69 444 444 444 450 ÷ 2 = 34 722 222 222 225 +
**0**; - 34 722 222 222 225 ÷ 2 = 17 361 111 111 112 +
**1**; - 17 361 111 111 112 ÷ 2 = 8 680 555 555 556 +
**0**; - 8 680 555 555 556 ÷ 2 = 4 340 277 777 778 +
**0**; - 4 340 277 777 778 ÷ 2 = 2 170 138 888 889 +
**0**; - 2 170 138 888 889 ÷ 2 = 1 085 069 444 444 +
**1**; - 1 085 069 444 444 ÷ 2 = 542 534 722 222 +
**0**; - 542 534 722 222 ÷ 2 = 271 267 361 111 +
**0**; - 271 267 361 111 ÷ 2 = 135 633 680 555 +
**1**; - 135 633 680 555 ÷ 2 = 67 816 840 277 +
**1**; - 67 816 840 277 ÷ 2 = 33 908 420 138 +
**1**; - 33 908 420 138 ÷ 2 = 16 954 210 069 +
**0**; - 16 954 210 069 ÷ 2 = 8 477 105 034 +
**1**; - 8 477 105 034 ÷ 2 = 4 238 552 517 +
**0**; - 4 238 552 517 ÷ 2 = 2 119 276 258 +
**1**; - 2 119 276 258 ÷ 2 = 1 059 638 129 +
**0**; - 1 059 638 129 ÷ 2 = 529 819 064 +
**1**; - 529 819 064 ÷ 2 = 264 909 532 +
**0**; - 264 909 532 ÷ 2 = 132 454 766 +
**0**; - 132 454 766 ÷ 2 = 66 227 383 +
**0**; - 66 227 383 ÷ 2 = 33 113 691 +
**1**; - 33 113 691 ÷ 2 = 16 556 845 +
**1**; - 16 556 845 ÷ 2 = 8 278 422 +
**1**; - 8 278 422 ÷ 2 = 4 139 211 +
**0**; - 4 139 211 ÷ 2 = 2 069 605 +
**1**; - 2 069 605 ÷ 2 = 1 034 802 +
**1**; - 1 034 802 ÷ 2 = 517 401 +
**0**; - 517 401 ÷ 2 = 258 700 +
**1**; - 258 700 ÷ 2 = 129 350 +
**0**; - 129 350 ÷ 2 = 64 675 +
**0**; - 64 675 ÷ 2 = 32 337 +
**1**; - 32 337 ÷ 2 = 16 168 +
**1**; - 16 168 ÷ 2 = 8 084 +
**0**; - 8 084 ÷ 2 = 4 042 +
**0**; - 4 042 ÷ 2 = 2 021 +
**0**; - 2 021 ÷ 2 = 1 010 +
**1**; - 1 010 ÷ 2 = 505 +
**0**; - 505 ÷ 2 = 252 +
**1**; - 252 ÷ 2 = 126 +
**0**; - 126 ÷ 2 = 63 +
**0**; - 63 ÷ 2 = 31 +
**1**; - 31 ÷ 2 = 15 +
**1**; - 15 ÷ 2 = 7 +
**1**; - 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.

#### 1 111 111 111 111 208_{(10)} = 11 1111 0010 1000 1100 1011 0111 0001 0101 0111 0010 0010 1000_{(2)}

### 3. Determine the signed binary number bit length:

#### The base 2 number's actual length, in bits: 50.

#### A signed binary's bit length must be equal to a power of 2, as of:

#### 2^{1} = 2; 2^{2} = 4; 2^{3} = 8; 2^{4} = 16; 2^{5} = 32; 2^{6} = 64; ...

#### The first bit (the leftmost) indicates the sign:

#### 0 = positive integer number, 1 = negative integer number

#### The least number that is:

#### 1) a power of 2

#### 2) and is larger than the actual length, 50,

#### 3) so that the first bit (leftmost) could be zero

(we deal with a positive number at this moment)

#### === is: 64.

### 4. Get the positive binary computer representation on 64 bits (8 Bytes):

#### If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.

## Number 1 111 111 111 111 208_{(10)}, a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

## 1 111 111 111 111 208_{(10)} = 0000 0000 0000 0011 1111 0010 1000 1100 1011 0111 0001 0101 0111 0010 0010 1000

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