### 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**; - 11 000 011 100 001 188 ÷ 2 = 5 500 005 550 000 594 +
**0**; - 5 500 005 550 000 594 ÷ 2 = 2 750 002 775 000 297 +
**0**; - 2 750 002 775 000 297 ÷ 2 = 1 375 001 387 500 148 +
**1**; - 1 375 001 387 500 148 ÷ 2 = 687 500 693 750 074 +
**0**; - 687 500 693 750 074 ÷ 2 = 343 750 346 875 037 +
**0**; - 343 750 346 875 037 ÷ 2 = 171 875 173 437 518 +
**1**; - 171 875 173 437 518 ÷ 2 = 85 937 586 718 759 +
**0**; - 85 937 586 718 759 ÷ 2 = 42 968 793 359 379 +
**1**; - 42 968 793 359 379 ÷ 2 = 21 484 396 679 689 +
**1**; - 21 484 396 679 689 ÷ 2 = 10 742 198 339 844 +
**1**; - 10 742 198 339 844 ÷ 2 = 5 371 099 169 922 +
**0**; - 5 371 099 169 922 ÷ 2 = 2 685 549 584 961 +
**0**; - 2 685 549 584 961 ÷ 2 = 1 342 774 792 480 +
**1**; - 1 342 774 792 480 ÷ 2 = 671 387 396 240 +
**0**; - 671 387 396 240 ÷ 2 = 335 693 698 120 +
**0**; - 335 693 698 120 ÷ 2 = 167 846 849 060 +
**0**; - 167 846 849 060 ÷ 2 = 83 923 424 530 +
**0**; - 83 923 424 530 ÷ 2 = 41 961 712 265 +
**0**; - 41 961 712 265 ÷ 2 = 20 980 856 132 +
**1**; - 20 980 856 132 ÷ 2 = 10 490 428 066 +
**0**; - 10 490 428 066 ÷ 2 = 5 245 214 033 +
**0**; - 5 245 214 033 ÷ 2 = 2 622 607 016 +
**1**; - 2 622 607 016 ÷ 2 = 1 311 303 508 +
**0**; - 1 311 303 508 ÷ 2 = 655 651 754 +
**0**; - 655 651 754 ÷ 2 = 327 825 877 +
**0**; - 327 825 877 ÷ 2 = 163 912 938 +
**1**; - 163 912 938 ÷ 2 = 81 956 469 +
**0**; - 81 956 469 ÷ 2 = 40 978 234 +
**1**; - 40 978 234 ÷ 2 = 20 489 117 +
**0**; - 20 489 117 ÷ 2 = 10 244 558 +
**1**; - 10 244 558 ÷ 2 = 5 122 279 +
**0**; - 5 122 279 ÷ 2 = 2 561 139 +
**1**; - 2 561 139 ÷ 2 = 1 280 569 +
**1**; - 1 280 569 ÷ 2 = 640 284 +
**1**; - 640 284 ÷ 2 = 320 142 +
**0**; - 320 142 ÷ 2 = 160 071 +
**0**; - 160 071 ÷ 2 = 80 035 +
**1**; - 80 035 ÷ 2 = 40 017 +
**1**; - 40 017 ÷ 2 = 20 008 +
**1**; - 20 008 ÷ 2 = 10 004 +
**0**; - 10 004 ÷ 2 = 5 002 +
**0**; - 5 002 ÷ 2 = 2 501 +
**0**; - 2 501 ÷ 2 = 1 250 +
**1**; - 1 250 ÷ 2 = 625 +
**0**; - 625 ÷ 2 = 312 +
**1**; - 312 ÷ 2 = 156 +
**0**; - 156 ÷ 2 = 78 +
**0**; - 78 ÷ 2 = 39 +
**0**; - 39 ÷ 2 = 19 +
**1**; - 19 ÷ 2 = 9 +
**1**; - 9 ÷ 2 = 4 +
**1**; - 4 ÷ 2 = 2 +
**0**; - 2 ÷ 2 = 1 +
**0**; - 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.

#### 11 000 011 100 001 188_{(10)} = 10 0111 0001 0100 0111 0011 1010 1010 0010 0100 0001 0011 1010 0100_{(2)}

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

#### The base 2 number's actual length, in bits: 54.

#### 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, 54,

#### 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 11 000 011 100 001 188_{(10)}, a signed integer number (with sign),

converted from decimal system (from base 10)

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

## 11 000 011 100 001 188_{(10)} = 0000 0000 0010 0111 0001 0100 0111 0011 1010 1010 0010 0100 0001 0011 1010 0100

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