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;
- 1 456 777 255 814 994 ÷ 2 = 728 388 627 907 497 + 0;
- 728 388 627 907 497 ÷ 2 = 364 194 313 953 748 + 1;
- 364 194 313 953 748 ÷ 2 = 182 097 156 976 874 + 0;
- 182 097 156 976 874 ÷ 2 = 91 048 578 488 437 + 0;
- 91 048 578 488 437 ÷ 2 = 45 524 289 244 218 + 1;
- 45 524 289 244 218 ÷ 2 = 22 762 144 622 109 + 0;
- 22 762 144 622 109 ÷ 2 = 11 381 072 311 054 + 1;
- 11 381 072 311 054 ÷ 2 = 5 690 536 155 527 + 0;
- 5 690 536 155 527 ÷ 2 = 2 845 268 077 763 + 1;
- 2 845 268 077 763 ÷ 2 = 1 422 634 038 881 + 1;
- 1 422 634 038 881 ÷ 2 = 711 317 019 440 + 1;
- 711 317 019 440 ÷ 2 = 355 658 509 720 + 0;
- 355 658 509 720 ÷ 2 = 177 829 254 860 + 0;
- 177 829 254 860 ÷ 2 = 88 914 627 430 + 0;
- 88 914 627 430 ÷ 2 = 44 457 313 715 + 0;
- 44 457 313 715 ÷ 2 = 22 228 656 857 + 1;
- 22 228 656 857 ÷ 2 = 11 114 328 428 + 1;
- 11 114 328 428 ÷ 2 = 5 557 164 214 + 0;
- 5 557 164 214 ÷ 2 = 2 778 582 107 + 0;
- 2 778 582 107 ÷ 2 = 1 389 291 053 + 1;
- 1 389 291 053 ÷ 2 = 694 645 526 + 1;
- 694 645 526 ÷ 2 = 347 322 763 + 0;
- 347 322 763 ÷ 2 = 173 661 381 + 1;
- 173 661 381 ÷ 2 = 86 830 690 + 1;
- 86 830 690 ÷ 2 = 43 415 345 + 0;
- 43 415 345 ÷ 2 = 21 707 672 + 1;
- 21 707 672 ÷ 2 = 10 853 836 + 0;
- 10 853 836 ÷ 2 = 5 426 918 + 0;
- 5 426 918 ÷ 2 = 2 713 459 + 0;
- 2 713 459 ÷ 2 = 1 356 729 + 1;
- 1 356 729 ÷ 2 = 678 364 + 1;
- 678 364 ÷ 2 = 339 182 + 0;
- 339 182 ÷ 2 = 169 591 + 0;
- 169 591 ÷ 2 = 84 795 + 1;
- 84 795 ÷ 2 = 42 397 + 1;
- 42 397 ÷ 2 = 21 198 + 1;
- 21 198 ÷ 2 = 10 599 + 0;
- 10 599 ÷ 2 = 5 299 + 1;
- 5 299 ÷ 2 = 2 649 + 1;
- 2 649 ÷ 2 = 1 324 + 1;
- 1 324 ÷ 2 = 662 + 0;
- 662 ÷ 2 = 331 + 0;
- 331 ÷ 2 = 165 + 1;
- 165 ÷ 2 = 82 + 1;
- 82 ÷ 2 = 41 + 0;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
1 456 777 255 814 994(10) = 101 0010 1100 1110 1110 0110 0010 1101 1001 1000 0111 0101 0010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 51.
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) 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, 51,
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 1 456 777 255 814 994(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
1 456 777 255 814 994(10) = 0000 0000 0000 0101 0010 1100 1110 1110 0110 0010 1101 1001 1000 0111 0101 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.