1. Start with the positive version of the number:
|-4 608 353 354 703 133 778| = 4 608 353 354 703 133 778
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;
- 4 608 353 354 703 133 778 ÷ 2 = 2 304 176 677 351 566 889 + 0;
- 2 304 176 677 351 566 889 ÷ 2 = 1 152 088 338 675 783 444 + 1;
- 1 152 088 338 675 783 444 ÷ 2 = 576 044 169 337 891 722 + 0;
- 576 044 169 337 891 722 ÷ 2 = 288 022 084 668 945 861 + 0;
- 288 022 084 668 945 861 ÷ 2 = 144 011 042 334 472 930 + 1;
- 144 011 042 334 472 930 ÷ 2 = 72 005 521 167 236 465 + 0;
- 72 005 521 167 236 465 ÷ 2 = 36 002 760 583 618 232 + 1;
- 36 002 760 583 618 232 ÷ 2 = 18 001 380 291 809 116 + 0;
- 18 001 380 291 809 116 ÷ 2 = 9 000 690 145 904 558 + 0;
- 9 000 690 145 904 558 ÷ 2 = 4 500 345 072 952 279 + 0;
- 4 500 345 072 952 279 ÷ 2 = 2 250 172 536 476 139 + 1;
- 2 250 172 536 476 139 ÷ 2 = 1 125 086 268 238 069 + 1;
- 1 125 086 268 238 069 ÷ 2 = 562 543 134 119 034 + 1;
- 562 543 134 119 034 ÷ 2 = 281 271 567 059 517 + 0;
- 281 271 567 059 517 ÷ 2 = 140 635 783 529 758 + 1;
- 140 635 783 529 758 ÷ 2 = 70 317 891 764 879 + 0;
- 70 317 891 764 879 ÷ 2 = 35 158 945 882 439 + 1;
- 35 158 945 882 439 ÷ 2 = 17 579 472 941 219 + 1;
- 17 579 472 941 219 ÷ 2 = 8 789 736 470 609 + 1;
- 8 789 736 470 609 ÷ 2 = 4 394 868 235 304 + 1;
- 4 394 868 235 304 ÷ 2 = 2 197 434 117 652 + 0;
- 2 197 434 117 652 ÷ 2 = 1 098 717 058 826 + 0;
- 1 098 717 058 826 ÷ 2 = 549 358 529 413 + 0;
- 549 358 529 413 ÷ 2 = 274 679 264 706 + 1;
- 274 679 264 706 ÷ 2 = 137 339 632 353 + 0;
- 137 339 632 353 ÷ 2 = 68 669 816 176 + 1;
- 68 669 816 176 ÷ 2 = 34 334 908 088 + 0;
- 34 334 908 088 ÷ 2 = 17 167 454 044 + 0;
- 17 167 454 044 ÷ 2 = 8 583 727 022 + 0;
- 8 583 727 022 ÷ 2 = 4 291 863 511 + 0;
- 4 291 863 511 ÷ 2 = 2 145 931 755 + 1;
- 2 145 931 755 ÷ 2 = 1 072 965 877 + 1;
- 1 072 965 877 ÷ 2 = 536 482 938 + 1;
- 536 482 938 ÷ 2 = 268 241 469 + 0;
- 268 241 469 ÷ 2 = 134 120 734 + 1;
- 134 120 734 ÷ 2 = 67 060 367 + 0;
- 67 060 367 ÷ 2 = 33 530 183 + 1;
- 33 530 183 ÷ 2 = 16 765 091 + 1;
- 16 765 091 ÷ 2 = 8 382 545 + 1;
- 8 382 545 ÷ 2 = 4 191 272 + 1;
- 4 191 272 ÷ 2 = 2 095 636 + 0;
- 2 095 636 ÷ 2 = 1 047 818 + 0;
- 1 047 818 ÷ 2 = 523 909 + 0;
- 523 909 ÷ 2 = 261 954 + 1;
- 261 954 ÷ 2 = 130 977 + 0;
- 130 977 ÷ 2 = 65 488 + 1;
- 65 488 ÷ 2 = 32 744 + 0;
- 32 744 ÷ 2 = 16 372 + 0;
- 16 372 ÷ 2 = 8 186 + 0;
- 8 186 ÷ 2 = 4 093 + 0;
- 4 093 ÷ 2 = 2 046 + 1;
- 2 046 ÷ 2 = 1 023 + 0;
- 1 023 ÷ 2 = 511 + 1;
- 511 ÷ 2 = 255 + 1;
- 255 ÷ 2 = 127 + 1;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 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.
4 608 353 354 703 133 778(10) = 11 1111 1111 0100 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 0101 0010(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 62.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 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, 62,
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:
4 608 353 354 703 133 778(10) = 0011 1111 1111 0100 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 0101 0010
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 -4 608 353 354 703 133 778(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-4 608 353 354 703 133 778(10) = 1011 1111 1111 0100 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 0101 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.