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;
- 10 101 011 009 992 ÷ 2 = 5 050 505 504 996 + 0;
- 5 050 505 504 996 ÷ 2 = 2 525 252 752 498 + 0;
- 2 525 252 752 498 ÷ 2 = 1 262 626 376 249 + 0;
- 1 262 626 376 249 ÷ 2 = 631 313 188 124 + 1;
- 631 313 188 124 ÷ 2 = 315 656 594 062 + 0;
- 315 656 594 062 ÷ 2 = 157 828 297 031 + 0;
- 157 828 297 031 ÷ 2 = 78 914 148 515 + 1;
- 78 914 148 515 ÷ 2 = 39 457 074 257 + 1;
- 39 457 074 257 ÷ 2 = 19 728 537 128 + 1;
- 19 728 537 128 ÷ 2 = 9 864 268 564 + 0;
- 9 864 268 564 ÷ 2 = 4 932 134 282 + 0;
- 4 932 134 282 ÷ 2 = 2 466 067 141 + 0;
- 2 466 067 141 ÷ 2 = 1 233 033 570 + 1;
- 1 233 033 570 ÷ 2 = 616 516 785 + 0;
- 616 516 785 ÷ 2 = 308 258 392 + 1;
- 308 258 392 ÷ 2 = 154 129 196 + 0;
- 154 129 196 ÷ 2 = 77 064 598 + 0;
- 77 064 598 ÷ 2 = 38 532 299 + 0;
- 38 532 299 ÷ 2 = 19 266 149 + 1;
- 19 266 149 ÷ 2 = 9 633 074 + 1;
- 9 633 074 ÷ 2 = 4 816 537 + 0;
- 4 816 537 ÷ 2 = 2 408 268 + 1;
- 2 408 268 ÷ 2 = 1 204 134 + 0;
- 1 204 134 ÷ 2 = 602 067 + 0;
- 602 067 ÷ 2 = 301 033 + 1;
- 301 033 ÷ 2 = 150 516 + 1;
- 150 516 ÷ 2 = 75 258 + 0;
- 75 258 ÷ 2 = 37 629 + 0;
- 37 629 ÷ 2 = 18 814 + 1;
- 18 814 ÷ 2 = 9 407 + 0;
- 9 407 ÷ 2 = 4 703 + 1;
- 4 703 ÷ 2 = 2 351 + 1;
- 2 351 ÷ 2 = 1 175 + 1;
- 1 175 ÷ 2 = 587 + 1;
- 587 ÷ 2 = 293 + 1;
- 293 ÷ 2 = 146 + 1;
- 146 ÷ 2 = 73 + 0;
- 73 ÷ 2 = 36 + 1;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 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.
10 101 011 009 992(10) = 1001 0010 1111 1101 0011 0010 1100 0101 0001 1100 1000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 44.
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, 44,
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 10 101 011 009 992(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:
10 101 011 009 992(10) = 0000 0000 0000 0000 0000 1001 0010 1111 1101 0011 0010 1100 0101 0001 1100 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.