### 2. 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**; - 4 611 686 018 427 388 003 ÷ 2 = 2 305 843 009 213 694 001 +
**1**; - 2 305 843 009 213 694 001 ÷ 2 = 1 152 921 504 606 847 000 +
**1**; - 1 152 921 504 606 847 000 ÷ 2 = 576 460 752 303 423 500 +
**0**; - 576 460 752 303 423 500 ÷ 2 = 288 230 376 151 711 750 +
**0**; - 288 230 376 151 711 750 ÷ 2 = 144 115 188 075 855 875 +
**0**; - 144 115 188 075 855 875 ÷ 2 = 72 057 594 037 927 937 +
**1**; - 72 057 594 037 927 937 ÷ 2 = 36 028 797 018 963 968 +
**1**; - 36 028 797 018 963 968 ÷ 2 = 18 014 398 509 481 984 +
**0**; - 18 014 398 509 481 984 ÷ 2 = 9 007 199 254 740 992 +
**0**; - 9 007 199 254 740 992 ÷ 2 = 4 503 599 627 370 496 +
**0**; - 4 503 599 627 370 496 ÷ 2 = 2 251 799 813 685 248 +
**0**; - 2 251 799 813 685 248 ÷ 2 = 1 125 899 906 842 624 +
**0**; - 1 125 899 906 842 624 ÷ 2 = 562 949 953 421 312 +
**0**; - 562 949 953 421 312 ÷ 2 = 281 474 976 710 656 +
**0**; - 281 474 976 710 656 ÷ 2 = 140 737 488 355 328 +
**0**; - 140 737 488 355 328 ÷ 2 = 70 368 744 177 664 +
**0**; - 70 368 744 177 664 ÷ 2 = 35 184 372 088 832 +
**0**; - 35 184 372 088 832 ÷ 2 = 17 592 186 044 416 +
**0**; - 17 592 186 044 416 ÷ 2 = 8 796 093 022 208 +
**0**; - 8 796 093 022 208 ÷ 2 = 4 398 046 511 104 +
**0**; - 4 398 046 511 104 ÷ 2 = 2 199 023 255 552 +
**0**; - 2 199 023 255 552 ÷ 2 = 1 099 511 627 776 +
**0**; - 1 099 511 627 776 ÷ 2 = 549 755 813 888 +
**0**; - 549 755 813 888 ÷ 2 = 274 877 906 944 +
**0**; - 274 877 906 944 ÷ 2 = 137 438 953 472 +
**0**; - 137 438 953 472 ÷ 2 = 68 719 476 736 +
**0**; - 68 719 476 736 ÷ 2 = 34 359 738 368 +
**0**; - 34 359 738 368 ÷ 2 = 17 179 869 184 +
**0**; - 17 179 869 184 ÷ 2 = 8 589 934 592 +
**0**; - 8 589 934 592 ÷ 2 = 4 294 967 296 +
**0**; - 4 294 967 296 ÷ 2 = 2 147 483 648 +
**0**; - 2 147 483 648 ÷ 2 = 1 073 741 824 +
**0**; - 1 073 741 824 ÷ 2 = 536 870 912 +
**0**; - 536 870 912 ÷ 2 = 268 435 456 +
**0**; - 268 435 456 ÷ 2 = 134 217 728 +
**0**; - 134 217 728 ÷ 2 = 67 108 864 +
**0**; - 67 108 864 ÷ 2 = 33 554 432 +
**0**; - 33 554 432 ÷ 2 = 16 777 216 +
**0**; - 16 777 216 ÷ 2 = 8 388 608 +
**0**; - 8 388 608 ÷ 2 = 4 194 304 +
**0**; - 4 194 304 ÷ 2 = 2 097 152 +
**0**; - 2 097 152 ÷ 2 = 1 048 576 +
**0**; - 1 048 576 ÷ 2 = 524 288 +
**0**; - 524 288 ÷ 2 = 262 144 +
**0**; - 262 144 ÷ 2 = 131 072 +
**0**; - 131 072 ÷ 2 = 65 536 +
**0**; - 65 536 ÷ 2 = 32 768 +
**0**; - 32 768 ÷ 2 = 16 384 +
**0**; - 16 384 ÷ 2 = 8 192 +
**0**; - 8 192 ÷ 2 = 4 096 +
**0**; - 4 096 ÷ 2 = 2 048 +
**0**; - 2 048 ÷ 2 = 1 024 +
**0**; - 1 024 ÷ 2 = 512 +
**0**; - 512 ÷ 2 = 256 +
**0**; - 256 ÷ 2 = 128 +
**0**; - 128 ÷ 2 = 64 +
**0**; - 64 ÷ 2 = 32 +
**0**; - 32 ÷ 2 = 16 +
**0**; - 16 ÷ 2 = 8 +
**0**; - 8 ÷ 2 = 4 +
**0**; - 4 ÷ 2 = 2 +
**0**; - 2 ÷ 2 = 1 +
**0**; - 1 ÷ 2 = 0 +
**1**;

### 3. Construct the base 2 representation of the positive number:

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

#### 4 611 686 018 427 388 003_{(10)} = 100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0110 0011_{(2)}

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

#### The base 2 number's actual length, in bits: 63.

#### 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, 63,

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

(we deal with a positive number at this moment)

#### === is: 64.

### 5. 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:

#### 4 611 686 018 427 388 003_{(10)} = 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0110 0011

### 6. Get the negative integer number representation:

#### To get the negative integer number representation on 64 bits (8 Bytes),

#### ... change the first bit (the leftmost), from 0 to 1...

## Number -4 611 686 018 427 388 003_{(10)}, a signed integer number (with sign),

converted from decimal system (from base 10)

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

## -4 611 686 018 427 388 003_{(10)} = 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0110 0011

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