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;
- 587 447 586 981 ÷ 2 = 293 723 793 490 + 1;
- 293 723 793 490 ÷ 2 = 146 861 896 745 + 0;
- 146 861 896 745 ÷ 2 = 73 430 948 372 + 1;
- 73 430 948 372 ÷ 2 = 36 715 474 186 + 0;
- 36 715 474 186 ÷ 2 = 18 357 737 093 + 0;
- 18 357 737 093 ÷ 2 = 9 178 868 546 + 1;
- 9 178 868 546 ÷ 2 = 4 589 434 273 + 0;
- 4 589 434 273 ÷ 2 = 2 294 717 136 + 1;
- 2 294 717 136 ÷ 2 = 1 147 358 568 + 0;
- 1 147 358 568 ÷ 2 = 573 679 284 + 0;
- 573 679 284 ÷ 2 = 286 839 642 + 0;
- 286 839 642 ÷ 2 = 143 419 821 + 0;
- 143 419 821 ÷ 2 = 71 709 910 + 1;
- 71 709 910 ÷ 2 = 35 854 955 + 0;
- 35 854 955 ÷ 2 = 17 927 477 + 1;
- 17 927 477 ÷ 2 = 8 963 738 + 1;
- 8 963 738 ÷ 2 = 4 481 869 + 0;
- 4 481 869 ÷ 2 = 2 240 934 + 1;
- 2 240 934 ÷ 2 = 1 120 467 + 0;
- 1 120 467 ÷ 2 = 560 233 + 1;
- 560 233 ÷ 2 = 280 116 + 1;
- 280 116 ÷ 2 = 140 058 + 0;
- 140 058 ÷ 2 = 70 029 + 0;
- 70 029 ÷ 2 = 35 014 + 1;
- 35 014 ÷ 2 = 17 507 + 0;
- 17 507 ÷ 2 = 8 753 + 1;
- 8 753 ÷ 2 = 4 376 + 1;
- 4 376 ÷ 2 = 2 188 + 0;
- 2 188 ÷ 2 = 1 094 + 0;
- 1 094 ÷ 2 = 547 + 0;
- 547 ÷ 2 = 273 + 1;
- 273 ÷ 2 = 136 + 1;
- 136 ÷ 2 = 68 + 0;
- 68 ÷ 2 = 34 + 0;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 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.
587 447 586 981(10) = 1000 1000 1100 0110 1001 1010 1101 0000 1010 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 40.
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, 40,
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 587 447 586 981(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
587 447 586 981(10) = 0000 0000 0000 0000 0000 0000 1000 1000 1100 0110 1001 1010 1101 0000 1010 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.