### 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**; - 496 916 632 435 730 664 ÷ 2 = 248 458 316 217 865 332 +
**0**; - 248 458 316 217 865 332 ÷ 2 = 124 229 158 108 932 666 +
**0**; - 124 229 158 108 932 666 ÷ 2 = 62 114 579 054 466 333 +
**0**; - 62 114 579 054 466 333 ÷ 2 = 31 057 289 527 233 166 +
**1**; - 31 057 289 527 233 166 ÷ 2 = 15 528 644 763 616 583 +
**0**; - 15 528 644 763 616 583 ÷ 2 = 7 764 322 381 808 291 +
**1**; - 7 764 322 381 808 291 ÷ 2 = 3 882 161 190 904 145 +
**1**; - 3 882 161 190 904 145 ÷ 2 = 1 941 080 595 452 072 +
**1**; - 1 941 080 595 452 072 ÷ 2 = 970 540 297 726 036 +
**0**; - 970 540 297 726 036 ÷ 2 = 485 270 148 863 018 +
**0**; - 485 270 148 863 018 ÷ 2 = 242 635 074 431 509 +
**0**; - 242 635 074 431 509 ÷ 2 = 121 317 537 215 754 +
**1**; - 121 317 537 215 754 ÷ 2 = 60 658 768 607 877 +
**0**; - 60 658 768 607 877 ÷ 2 = 30 329 384 303 938 +
**1**; - 30 329 384 303 938 ÷ 2 = 15 164 692 151 969 +
**0**; - 15 164 692 151 969 ÷ 2 = 7 582 346 075 984 +
**1**; - 7 582 346 075 984 ÷ 2 = 3 791 173 037 992 +
**0**; - 3 791 173 037 992 ÷ 2 = 1 895 586 518 996 +
**0**; - 1 895 586 518 996 ÷ 2 = 947 793 259 498 +
**0**; - 947 793 259 498 ÷ 2 = 473 896 629 749 +
**0**; - 473 896 629 749 ÷ 2 = 236 948 314 874 +
**1**; - 236 948 314 874 ÷ 2 = 118 474 157 437 +
**0**; - 118 474 157 437 ÷ 2 = 59 237 078 718 +
**1**; - 59 237 078 718 ÷ 2 = 29 618 539 359 +
**0**; - 29 618 539 359 ÷ 2 = 14 809 269 679 +
**1**; - 14 809 269 679 ÷ 2 = 7 404 634 839 +
**1**; - 7 404 634 839 ÷ 2 = 3 702 317 419 +
**1**; - 3 702 317 419 ÷ 2 = 1 851 158 709 +
**1**; - 1 851 158 709 ÷ 2 = 925 579 354 +
**1**; - 925 579 354 ÷ 2 = 462 789 677 +
**0**; - 462 789 677 ÷ 2 = 231 394 838 +
**1**; - 231 394 838 ÷ 2 = 115 697 419 +
**0**; - 115 697 419 ÷ 2 = 57 848 709 +
**1**; - 57 848 709 ÷ 2 = 28 924 354 +
**1**; - 28 924 354 ÷ 2 = 14 462 177 +
**0**; - 14 462 177 ÷ 2 = 7 231 088 +
**1**; - 7 231 088 ÷ 2 = 3 615 544 +
**0**; - 3 615 544 ÷ 2 = 1 807 772 +
**0**; - 1 807 772 ÷ 2 = 903 886 +
**0**; - 903 886 ÷ 2 = 451 943 +
**0**; - 451 943 ÷ 2 = 225 971 +
**1**; - 225 971 ÷ 2 = 112 985 +
**1**; - 112 985 ÷ 2 = 56 492 +
**1**; - 56 492 ÷ 2 = 28 246 +
**0**; - 28 246 ÷ 2 = 14 123 +
**0**; - 14 123 ÷ 2 = 7 061 +
**1**; - 7 061 ÷ 2 = 3 530 +
**1**; - 3 530 ÷ 2 = 1 765 +
**0**; - 1 765 ÷ 2 = 882 +
**1**; - 882 ÷ 2 = 441 +
**0**; - 441 ÷ 2 = 220 +
**1**; - 220 ÷ 2 = 110 +
**0**; - 110 ÷ 2 = 55 +
**0**; - 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 number:

#### Take all the remainders starting from the bottom of the list constructed above.

#### 496 916 632 435 730 664_{(10)} = 110 1110 0101 0110 0111 0000 1011 0101 1111 0101 0000 1010 1000 1110 1000_{(2)}

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

#### The base 2 number's actual length, in bits: 59.

#### 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, 59,

#### 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 496 916 632 435 730 664_{(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:

## 496 916 632 435 730 664_{(10)} = 0000 0110 1110 0101 0110 0111 0000 1011 0101 1111 0101 0000 1010 1000 1110 1000

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