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;
- 1 010 100 100 000 130 ÷ 2 = 505 050 050 000 065 + 0;
- 505 050 050 000 065 ÷ 2 = 252 525 025 000 032 + 1;
- 252 525 025 000 032 ÷ 2 = 126 262 512 500 016 + 0;
- 126 262 512 500 016 ÷ 2 = 63 131 256 250 008 + 0;
- 63 131 256 250 008 ÷ 2 = 31 565 628 125 004 + 0;
- 31 565 628 125 004 ÷ 2 = 15 782 814 062 502 + 0;
- 15 782 814 062 502 ÷ 2 = 7 891 407 031 251 + 0;
- 7 891 407 031 251 ÷ 2 = 3 945 703 515 625 + 1;
- 3 945 703 515 625 ÷ 2 = 1 972 851 757 812 + 1;
- 1 972 851 757 812 ÷ 2 = 986 425 878 906 + 0;
- 986 425 878 906 ÷ 2 = 493 212 939 453 + 0;
- 493 212 939 453 ÷ 2 = 246 606 469 726 + 1;
- 246 606 469 726 ÷ 2 = 123 303 234 863 + 0;
- 123 303 234 863 ÷ 2 = 61 651 617 431 + 1;
- 61 651 617 431 ÷ 2 = 30 825 808 715 + 1;
- 30 825 808 715 ÷ 2 = 15 412 904 357 + 1;
- 15 412 904 357 ÷ 2 = 7 706 452 178 + 1;
- 7 706 452 178 ÷ 2 = 3 853 226 089 + 0;
- 3 853 226 089 ÷ 2 = 1 926 613 044 + 1;
- 1 926 613 044 ÷ 2 = 963 306 522 + 0;
- 963 306 522 ÷ 2 = 481 653 261 + 0;
- 481 653 261 ÷ 2 = 240 826 630 + 1;
- 240 826 630 ÷ 2 = 120 413 315 + 0;
- 120 413 315 ÷ 2 = 60 206 657 + 1;
- 60 206 657 ÷ 2 = 30 103 328 + 1;
- 30 103 328 ÷ 2 = 15 051 664 + 0;
- 15 051 664 ÷ 2 = 7 525 832 + 0;
- 7 525 832 ÷ 2 = 3 762 916 + 0;
- 3 762 916 ÷ 2 = 1 881 458 + 0;
- 1 881 458 ÷ 2 = 940 729 + 0;
- 940 729 ÷ 2 = 470 364 + 1;
- 470 364 ÷ 2 = 235 182 + 0;
- 235 182 ÷ 2 = 117 591 + 0;
- 117 591 ÷ 2 = 58 795 + 1;
- 58 795 ÷ 2 = 29 397 + 1;
- 29 397 ÷ 2 = 14 698 + 1;
- 14 698 ÷ 2 = 7 349 + 0;
- 7 349 ÷ 2 = 3 674 + 1;
- 3 674 ÷ 2 = 1 837 + 0;
- 1 837 ÷ 2 = 918 + 1;
- 918 ÷ 2 = 459 + 0;
- 459 ÷ 2 = 229 + 1;
- 229 ÷ 2 = 114 + 1;
- 114 ÷ 2 = 57 + 0;
- 57 ÷ 2 = 28 + 1;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 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.
1 010 100 100 000 130(10) = 11 1001 0110 1010 1110 0100 0001 1010 0101 1110 1001 1000 0010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 50.
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, 50,
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 1 010 100 100 000 130(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:
1 010 100 100 000 130(10) = 0000 0000 0000 0011 1001 0110 1010 1110 0100 0001 1010 0101 1110 1001 1000 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.