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;
- 35 482 157 703 228 288 ÷ 2 = 17 741 078 851 614 144 + 0;
- 17 741 078 851 614 144 ÷ 2 = 8 870 539 425 807 072 + 0;
- 8 870 539 425 807 072 ÷ 2 = 4 435 269 712 903 536 + 0;
- 4 435 269 712 903 536 ÷ 2 = 2 217 634 856 451 768 + 0;
- 2 217 634 856 451 768 ÷ 2 = 1 108 817 428 225 884 + 0;
- 1 108 817 428 225 884 ÷ 2 = 554 408 714 112 942 + 0;
- 554 408 714 112 942 ÷ 2 = 277 204 357 056 471 + 0;
- 277 204 357 056 471 ÷ 2 = 138 602 178 528 235 + 1;
- 138 602 178 528 235 ÷ 2 = 69 301 089 264 117 + 1;
- 69 301 089 264 117 ÷ 2 = 34 650 544 632 058 + 1;
- 34 650 544 632 058 ÷ 2 = 17 325 272 316 029 + 0;
- 17 325 272 316 029 ÷ 2 = 8 662 636 158 014 + 1;
- 8 662 636 158 014 ÷ 2 = 4 331 318 079 007 + 0;
- 4 331 318 079 007 ÷ 2 = 2 165 659 039 503 + 1;
- 2 165 659 039 503 ÷ 2 = 1 082 829 519 751 + 1;
- 1 082 829 519 751 ÷ 2 = 541 414 759 875 + 1;
- 541 414 759 875 ÷ 2 = 270 707 379 937 + 1;
- 270 707 379 937 ÷ 2 = 135 353 689 968 + 1;
- 135 353 689 968 ÷ 2 = 67 676 844 984 + 0;
- 67 676 844 984 ÷ 2 = 33 838 422 492 + 0;
- 33 838 422 492 ÷ 2 = 16 919 211 246 + 0;
- 16 919 211 246 ÷ 2 = 8 459 605 623 + 0;
- 8 459 605 623 ÷ 2 = 4 229 802 811 + 1;
- 4 229 802 811 ÷ 2 = 2 114 901 405 + 1;
- 2 114 901 405 ÷ 2 = 1 057 450 702 + 1;
- 1 057 450 702 ÷ 2 = 528 725 351 + 0;
- 528 725 351 ÷ 2 = 264 362 675 + 1;
- 264 362 675 ÷ 2 = 132 181 337 + 1;
- 132 181 337 ÷ 2 = 66 090 668 + 1;
- 66 090 668 ÷ 2 = 33 045 334 + 0;
- 33 045 334 ÷ 2 = 16 522 667 + 0;
- 16 522 667 ÷ 2 = 8 261 333 + 1;
- 8 261 333 ÷ 2 = 4 130 666 + 1;
- 4 130 666 ÷ 2 = 2 065 333 + 0;
- 2 065 333 ÷ 2 = 1 032 666 + 1;
- 1 032 666 ÷ 2 = 516 333 + 0;
- 516 333 ÷ 2 = 258 166 + 1;
- 258 166 ÷ 2 = 129 083 + 0;
- 129 083 ÷ 2 = 64 541 + 1;
- 64 541 ÷ 2 = 32 270 + 1;
- 32 270 ÷ 2 = 16 135 + 0;
- 16 135 ÷ 2 = 8 067 + 1;
- 8 067 ÷ 2 = 4 033 + 1;
- 4 033 ÷ 2 = 2 016 + 1;
- 2 016 ÷ 2 = 1 008 + 0;
- 1 008 ÷ 2 = 504 + 0;
- 504 ÷ 2 = 252 + 0;
- 252 ÷ 2 = 126 + 0;
- 126 ÷ 2 = 63 + 0;
- 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.
35 482 157 703 228 288(10) = 111 1110 0000 1110 1101 0101 1001 1101 1100 0011 1110 1011 1000 0000(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 55.
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, 55,
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:
35 482 157 703 228 288(10) = 0000 0000 0111 1110 0000 1110 1101 0101 1001 1101 1100 0011 1110 1011 1000 0000
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 -35 482 157 703 228 288(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-35 482 157 703 228 288(10) = 1000 0000 0111 1110 0000 1110 1101 0101 1001 1101 1100 0011 1110 1011 1000 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.