### 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**; - 1 000 000 001 110 074 ÷ 2 = 500 000 000 555 037 +
**0**; - 500 000 000 555 037 ÷ 2 = 250 000 000 277 518 +
**1**; - 250 000 000 277 518 ÷ 2 = 125 000 000 138 759 +
**0**; - 125 000 000 138 759 ÷ 2 = 62 500 000 069 379 +
**1**; - 62 500 000 069 379 ÷ 2 = 31 250 000 034 689 +
**1**; - 31 250 000 034 689 ÷ 2 = 15 625 000 017 344 +
**1**; - 15 625 000 017 344 ÷ 2 = 7 812 500 008 672 +
**0**; - 7 812 500 008 672 ÷ 2 = 3 906 250 004 336 +
**0**; - 3 906 250 004 336 ÷ 2 = 1 953 125 002 168 +
**0**; - 1 953 125 002 168 ÷ 2 = 976 562 501 084 +
**0**; - 976 562 501 084 ÷ 2 = 488 281 250 542 +
**0**; - 488 281 250 542 ÷ 2 = 244 140 625 271 +
**0**; - 244 140 625 271 ÷ 2 = 122 070 312 635 +
**1**; - 122 070 312 635 ÷ 2 = 61 035 156 317 +
**1**; - 61 035 156 317 ÷ 2 = 30 517 578 158 +
**1**; - 30 517 578 158 ÷ 2 = 15 258 789 079 +
**0**; - 15 258 789 079 ÷ 2 = 7 629 394 539 +
**1**; - 7 629 394 539 ÷ 2 = 3 814 697 269 +
**1**; - 3 814 697 269 ÷ 2 = 1 907 348 634 +
**1**; - 1 907 348 634 ÷ 2 = 953 674 317 +
**0**; - 953 674 317 ÷ 2 = 476 837 158 +
**1**; - 476 837 158 ÷ 2 = 238 418 579 +
**0**; - 238 418 579 ÷ 2 = 119 209 289 +
**1**; - 119 209 289 ÷ 2 = 59 604 644 +
**1**; - 59 604 644 ÷ 2 = 29 802 322 +
**0**; - 29 802 322 ÷ 2 = 14 901 161 +
**0**; - 14 901 161 ÷ 2 = 7 450 580 +
**1**; - 7 450 580 ÷ 2 = 3 725 290 +
**0**; - 3 725 290 ÷ 2 = 1 862 645 +
**0**; - 1 862 645 ÷ 2 = 931 322 +
**1**; - 931 322 ÷ 2 = 465 661 +
**0**; - 465 661 ÷ 2 = 232 830 +
**1**; - 232 830 ÷ 2 = 116 415 +
**0**; - 116 415 ÷ 2 = 58 207 +
**1**; - 58 207 ÷ 2 = 29 103 +
**1**; - 29 103 ÷ 2 = 14 551 +
**1**; - 14 551 ÷ 2 = 7 275 +
**1**; - 7 275 ÷ 2 = 3 637 +
**1**; - 3 637 ÷ 2 = 1 818 +
**1**; - 1 818 ÷ 2 = 909 +
**0**; - 909 ÷ 2 = 454 +
**1**; - 454 ÷ 2 = 227 +
**0**; - 227 ÷ 2 = 113 +
**1**; - 113 ÷ 2 = 56 +
**1**; - 56 ÷ 2 = 28 +
**0**; - 28 ÷ 2 = 14 +
**0**; - 14 ÷ 2 = 7 +
**0**; - 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.

#### 1 000 000 001 110 074_{(10)} = 11 1000 1101 0111 1110 1010 0100 1101 0111 0111 0000 0011 1010_{(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) is reserved for 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 1 000 000 001 110 074_{(10)}, a signed integer number (with sign),

converted from decimal system (from base 10)

and written as a signed binary (in base 2):

## 1 000 000 001 110 074_{(10)} = 0000 0000 0000 0011 1000 1101 0111 1110 1010 0100 1101 0111 0111 0000 0011 1010

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