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;
- 9 218 868 437 227 405 396 ÷ 2 = 4 609 434 218 613 702 698 + 0;
- 4 609 434 218 613 702 698 ÷ 2 = 2 304 717 109 306 851 349 + 0;
- 2 304 717 109 306 851 349 ÷ 2 = 1 152 358 554 653 425 674 + 1;
- 1 152 358 554 653 425 674 ÷ 2 = 576 179 277 326 712 837 + 0;
- 576 179 277 326 712 837 ÷ 2 = 288 089 638 663 356 418 + 1;
- 288 089 638 663 356 418 ÷ 2 = 144 044 819 331 678 209 + 0;
- 144 044 819 331 678 209 ÷ 2 = 72 022 409 665 839 104 + 1;
- 72 022 409 665 839 104 ÷ 2 = 36 011 204 832 919 552 + 0;
- 36 011 204 832 919 552 ÷ 2 = 18 005 602 416 459 776 + 0;
- 18 005 602 416 459 776 ÷ 2 = 9 002 801 208 229 888 + 0;
- 9 002 801 208 229 888 ÷ 2 = 4 501 400 604 114 944 + 0;
- 4 501 400 604 114 944 ÷ 2 = 2 250 700 302 057 472 + 0;
- 2 250 700 302 057 472 ÷ 2 = 1 125 350 151 028 736 + 0;
- 1 125 350 151 028 736 ÷ 2 = 562 675 075 514 368 + 0;
- 562 675 075 514 368 ÷ 2 = 281 337 537 757 184 + 0;
- 281 337 537 757 184 ÷ 2 = 140 668 768 878 592 + 0;
- 140 668 768 878 592 ÷ 2 = 70 334 384 439 296 + 0;
- 70 334 384 439 296 ÷ 2 = 35 167 192 219 648 + 0;
- 35 167 192 219 648 ÷ 2 = 17 583 596 109 824 + 0;
- 17 583 596 109 824 ÷ 2 = 8 791 798 054 912 + 0;
- 8 791 798 054 912 ÷ 2 = 4 395 899 027 456 + 0;
- 4 395 899 027 456 ÷ 2 = 2 197 949 513 728 + 0;
- 2 197 949 513 728 ÷ 2 = 1 098 974 756 864 + 0;
- 1 098 974 756 864 ÷ 2 = 549 487 378 432 + 0;
- 549 487 378 432 ÷ 2 = 274 743 689 216 + 0;
- 274 743 689 216 ÷ 2 = 137 371 844 608 + 0;
- 137 371 844 608 ÷ 2 = 68 685 922 304 + 0;
- 68 685 922 304 ÷ 2 = 34 342 961 152 + 0;
- 34 342 961 152 ÷ 2 = 17 171 480 576 + 0;
- 17 171 480 576 ÷ 2 = 8 585 740 288 + 0;
- 8 585 740 288 ÷ 2 = 4 292 870 144 + 0;
- 4 292 870 144 ÷ 2 = 2 146 435 072 + 0;
- 2 146 435 072 ÷ 2 = 1 073 217 536 + 0;
- 1 073 217 536 ÷ 2 = 536 608 768 + 0;
- 536 608 768 ÷ 2 = 268 304 384 + 0;
- 268 304 384 ÷ 2 = 134 152 192 + 0;
- 134 152 192 ÷ 2 = 67 076 096 + 0;
- 67 076 096 ÷ 2 = 33 538 048 + 0;
- 33 538 048 ÷ 2 = 16 769 024 + 0;
- 16 769 024 ÷ 2 = 8 384 512 + 0;
- 8 384 512 ÷ 2 = 4 192 256 + 0;
- 4 192 256 ÷ 2 = 2 096 128 + 0;
- 2 096 128 ÷ 2 = 1 048 064 + 0;
- 1 048 064 ÷ 2 = 524 032 + 0;
- 524 032 ÷ 2 = 262 016 + 0;
- 262 016 ÷ 2 = 131 008 + 0;
- 131 008 ÷ 2 = 65 504 + 0;
- 65 504 ÷ 2 = 32 752 + 0;
- 32 752 ÷ 2 = 16 376 + 0;
- 16 376 ÷ 2 = 8 188 + 0;
- 8 188 ÷ 2 = 4 094 + 0;
- 4 094 ÷ 2 = 2 047 + 0;
- 2 047 ÷ 2 = 1 023 + 1;
- 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;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
9 218 868 437 227 405 396(10) = 111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0101 0100(2)
3. 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:
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, 63,
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 9 218 868 437 227 405 396(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:
9 218 868 437 227 405 396(10) = 0111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0101 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.