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;
- 1 001 100 999 903 ÷ 2 = 500 550 499 951 + 1;
- 500 550 499 951 ÷ 2 = 250 275 249 975 + 1;
- 250 275 249 975 ÷ 2 = 125 137 624 987 + 1;
- 125 137 624 987 ÷ 2 = 62 568 812 493 + 1;
- 62 568 812 493 ÷ 2 = 31 284 406 246 + 1;
- 31 284 406 246 ÷ 2 = 15 642 203 123 + 0;
- 15 642 203 123 ÷ 2 = 7 821 101 561 + 1;
- 7 821 101 561 ÷ 2 = 3 910 550 780 + 1;
- 3 910 550 780 ÷ 2 = 1 955 275 390 + 0;
- 1 955 275 390 ÷ 2 = 977 637 695 + 0;
- 977 637 695 ÷ 2 = 488 818 847 + 1;
- 488 818 847 ÷ 2 = 244 409 423 + 1;
- 244 409 423 ÷ 2 = 122 204 711 + 1;
- 122 204 711 ÷ 2 = 61 102 355 + 1;
- 61 102 355 ÷ 2 = 30 551 177 + 1;
- 30 551 177 ÷ 2 = 15 275 588 + 1;
- 15 275 588 ÷ 2 = 7 637 794 + 0;
- 7 637 794 ÷ 2 = 3 818 897 + 0;
- 3 818 897 ÷ 2 = 1 909 448 + 1;
- 1 909 448 ÷ 2 = 954 724 + 0;
- 954 724 ÷ 2 = 477 362 + 0;
- 477 362 ÷ 2 = 238 681 + 0;
- 238 681 ÷ 2 = 119 340 + 1;
- 119 340 ÷ 2 = 59 670 + 0;
- 59 670 ÷ 2 = 29 835 + 0;
- 29 835 ÷ 2 = 14 917 + 1;
- 14 917 ÷ 2 = 7 458 + 1;
- 7 458 ÷ 2 = 3 729 + 0;
- 3 729 ÷ 2 = 1 864 + 1;
- 1 864 ÷ 2 = 932 + 0;
- 932 ÷ 2 = 466 + 0;
- 466 ÷ 2 = 233 + 0;
- 233 ÷ 2 = 116 + 1;
- 116 ÷ 2 = 58 + 0;
- 58 ÷ 2 = 29 + 0;
- 29 ÷ 2 = 14 + 1;
- 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.
1 001 100 999 903(10) = 1110 1001 0001 0110 0100 0100 1111 1100 1101 1111(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) 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, 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 1 001 100 999 903(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
1 001 100 999 903(10) = 0000 0000 0000 0000 0000 0000 1110 1001 0001 0110 0100 0100 1111 1100 1101 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.